verify/ds/segtree/segtree_2d.test.cpp

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• Last update: 2026-10-06 01:57:24+09:00
• Problem: https://judge.yosupo.jp/problem/point_add_rectangle_sum

Depends on

• Segtree 2D (ds/segtree/segtree_2d.hpp)
• Bit Ceil (math/bit_ceil.hpp)
• Add Monoid (monoid/add.hpp)
• Monoid Concept (monoid/concept.hpp)
• Fast IO (utilities/fast_io.hpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/point_add_rectangle_sum"

#include "../../../ds/segtree/segtree_2d.hpp"
#include "../../../monoid/add.hpp"

#include <algorithm>
#include <cassert>
#include <cstdint>
#include "../../../utilities/fast_io.hpp"
#include <map>
#include <random>
#include <tuple>
#include <utility>
#include <vector>

using Sum = m1une::monoid::Add<long long>;

struct Query {
    int type;
    int first;
    int second;
    int third;
    int fourth;
    long long value;
};

#ifndef NDEBUG
void randomized_test() {
    std::mt19937 random(314159265);
    std::vector<std::pair<int, int>> points;
    std::map<std::pair<int, int>, long long> expected;
    for (int i = 0; i < 40; i++) {
        int x = int(random() % 15) - 7;
        int y = int(random() % 15) - 7;
        points.emplace_back(x, y);
        expected[{x, y}] = 0;
    }

    m1une::ds::Segtree2D<Sum> seg(points);
    assert(seg.size() == int(expected.size()));
    assert(!seg.contains_point(100, 100));
    assert(seg.get(100, 100) == 0);

    std::vector<std::pair<int, int>> distinct_points;
    for (const auto& [point, value] : expected) {
        (void)value;
        distinct_points.push_back(point);
    }

    for (int operation = 0; operation < 1000; operation++) {
        if (random() % 3 == 0) {
            auto point = distinct_points[random() % distinct_points.size()];
            long long value = int(random() % 101) - 50;
            seg.set(point.first, point.second, value);
            expected[point] = value;
            assert(seg(point.first, point.second) == value);
        } else {
            int x_lower = int(random() % 19) - 9;
            int x_upper = int(random() % 19) - 9;
            int y_lower = int(random() % 19) - 9;
            int y_upper = int(random() % 19) - 9;
            if (x_upper < x_lower) std::swap(x_lower, x_upper);
            if (y_upper < y_lower) std::swap(y_lower, y_upper);

            long long answer = 0;
            for (const auto& [point, value] : expected) {
                if (x_lower <= point.first && point.first < x_upper &&
                    y_lower <= point.second && point.second < y_upper) {
                    answer += value;
                }
            }
            assert(seg.prod(x_lower, x_upper, y_lower, y_upper) == answer);
        }
    }

    long long total = 0;
    for (const auto& [point, value] : expected) {
        (void)point;
        total += value;
    }
    assert(seg.all_prod() == total);
    auto values = seg.to_vector();
    assert(values.size() == expected.size());
    for (const auto& [x, y, value] : values) {
        std::pair<int, int> point(x, y);
        assert(expected[point] == value);
    }
}
#endif

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

#ifndef NDEBUG
    randomized_test();
#endif

    int n, q;
    fast_input >> n >> q;
    std::vector<std::tuple<int, int, long long>> initial(n);
    std::vector<std::pair<int, int>> points;
    points.reserve(n + q);
    for (auto& [x, y, weight] : initial) {
        fast_input >> x >> y >> weight;
        points.emplace_back(x, y);
    }

    std::vector<Query> queries(q);
    for (Query& query : queries) {
        fast_input >> query.type;
        if (query.type == 0) {
            fast_input >> query.first >> query.second >> query.value;
            query.third = query.fourth = 0;
            points.emplace_back(query.first, query.second);
        } else {
            fast_input >> query.first >> query.second >> query.third >> query.fourth;
            query.value = 0;
        }
    }

    m1une::ds::Segtree2D<Sum> seg(std::move(points));
    for (const auto& [x, y, weight] : initial) {
        seg.set(x, y, seg.get(x, y) + weight);
    }

    for (const Query& query : queries) {
        if (query.type == 0) {
            long long current = seg.get(query.first, query.second);
            seg.set(query.first, query.second, current + query.value);
        } else {
            fast_output << seg.prod(query.first, query.third, query.second, query.fourth)
                      << '\n';
        }
    }
}

#line 1 "verify/ds/segtree/segtree_2d.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/point_add_rectangle_sum"

#line 1 "ds/segtree/segtree_2d.hpp"



#include <algorithm>
#include <cassert>
#include <tuple>
#include <utility>
#include <vector>

#line 1 "math/bit_ceil.hpp"



namespace m1une {
namespace math {

template <typename T>
constexpr T bit_ceil(T n) {
    if (n <= 1) return 1;
    T x = 1;
    while (x < n) x <<= 1;
    return x;
}

}  // namespace math
}  // namespace m1une


#line 1 "monoid/concept.hpp"



#include <concepts>

namespace m1une {
namespace monoid {

// Concept to check if a type satisfies the requirements of a Monoid.
// A Monoid must have a `value_type`, an identity element `id()`, and an associative binary operation `op()`.
template <typename M>
concept IsMonoid = requires(typename M::value_type a, typename M::value_type b) {
    // 1. Must define `value_type`
    typename M::value_type;

    // 2. Must have a static method `id()` returning `value_type`
    { M::id() } -> std::same_as<typename M::value_type>;

    // 3. Must have a static method `op(a, b)` returning `value_type`
    { M::op(a, b) } -> std::same_as<typename M::value_type>;
};

// Concept for groups. A type satisfying this concept must also obey the group
// laws; concepts can check the interface but not the algebraic properties.
template <typename M>
concept IsGroup = IsMonoid<M> && requires(typename M::value_type a) {
    { M::inv(a) } -> std::same_as<typename M::value_type>;
};

// Concept for commutative groups. Commutativity is a semantic requirement and
// cannot be checked by a C++ concept.
template <typename M>
concept IsCommutativeGroup = IsGroup<M>;

}  // namespace monoid
}  // namespace m1une


#line 12 "ds/segtree/segtree_2d.hpp"

namespace m1une {
namespace ds {

// A static compressed 2D segment tree.
// It supports point assignment on registered points and rectangle product queries.
//
// The query rectangle is [xl, xr) x [yl, yr).
// All points that may be updated must be registered before construction.
template <class Monoid, class X = int, class Y = X>
requires m1une::monoid::IsMonoid<Monoid>
struct Segtree2D {
    using T = typename Monoid::value_type;
    using point_type = std::pair<X, Y>;
    using weighted_point_type = std::tuple<X, Y, T>;

private:
    int _n;
    int _size;
    int _point_count;
    std::vector<X> _xs;
    std::vector<std::vector<Y>> _ys;
    std::vector<std::vector<T>> _d;

    static std::vector<point_type> normalize_points(std::vector<point_type> points) {
        std::sort(points.begin(), points.end());
        points.erase(std::unique(points.begin(), points.end()), points.end());
        return points;
    }

    int x_index(const X& x) const {
        auto it = std::lower_bound(_xs.begin(), _xs.end(), x);
        if (it == _xs.end() || *it != x) return -1;
        return int(it - _xs.begin());
    }

    int y_index(int k, const Y& y) const {
        const auto& ys = _ys[k];
        auto it = std::lower_bound(ys.begin(), ys.end(), y);
        if (it == ys.end() || *it != y) return -1;
        return int(it - ys.begin());
    }

    T get_exact(int k, const Y& y) const {
        int pos = y_index(k, y);
        if (pos == -1) return Monoid::id();
        int m = int(_ys[k].size());
        return _d[k][m + pos];
    }

    void set_exact(int k, const Y& y, T x) {
        int pos = y_index(k, y);
        assert(pos != -1);

        int m = int(_ys[k].size());
        int p = m + pos;

        _d[k][p] = std::move(x);
        while (1 < p) {
            p >>= 1;
            _d[k][p] = Monoid::op(_d[k][2 * p], _d[k][2 * p + 1]);
        }
    }

    T prod_y(int k, const Y& yl, const Y& yr) const {
        assert(yl <= yr);
        if (yl == yr || _ys[k].empty()) return Monoid::id();

        const auto& ys = _ys[k];
        int l = int(std::lower_bound(ys.begin(), ys.end(), yl) - ys.begin());
        int r = int(std::lower_bound(ys.begin(), ys.end(), yr) - ys.begin());

        int m = int(ys.size());
        l += m;
        r += m;

        T sml = Monoid::id();
        T smr = Monoid::id();

        while (l < r) {
            if (l & 1) sml = Monoid::op(sml, _d[k][l++]);
            if (r & 1) smr = Monoid::op(_d[k][--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return Monoid::op(sml, smr);
    }

public:
    Segtree2D() : _n(0), _size(1), _point_count(0), _ys(2), _d(2) {}

    explicit Segtree2D(const std::vector<point_type>& points) {
        build(points);
    }

    explicit Segtree2D(std::vector<point_type>&& points) {
        build(std::move(points));
    }

    explicit Segtree2D(const std::vector<weighted_point_type>& points) {
        std::vector<point_type> coords;
        coords.reserve(points.size());

        for (const auto& [x, y, value] : points) {
            (void)value;
            coords.emplace_back(x, y);
        }

        build(std::move(coords));

        for (const auto& [x, y, value] : points) {
            set(x, y, value);
        }
    }

    void build(std::vector<point_type> points) {
        points = normalize_points(std::move(points));

        _point_count = int(points.size());

        _xs.clear();
        _xs.reserve(points.size());

        for (const auto& [x, y] : points) {
            (void)y;
            if (_xs.empty() || _xs.back() != x) _xs.push_back(x);
        }

        _n = int(_xs.size());
        _size = int(m1une::math::bit_ceil((unsigned int)std::max(1, _n)));

        _ys.assign(2 * _size, {});
        _d.assign(2 * _size, {});

        for (const auto& [x, y] : points) {
            int xi = int(std::lower_bound(_xs.begin(), _xs.end(), x) - _xs.begin());
            for (int k = xi + _size; k; k >>= 1) {
                _ys[k].push_back(y);
            }
        }

        for (int k = 1; k < 2 * _size; k++) {
            auto& ys = _ys[k];
            std::sort(ys.begin(), ys.end());
            ys.erase(std::unique(ys.begin(), ys.end()), ys.end());
            _d[k].assign(2 * ys.size(), Monoid::id());
        }
    }

    int size() const {
        return _point_count;
    }

    bool empty() const {
        return _point_count == 0;
    }

    int x_size() const {
        return _n;
    }

    const std::vector<X>& xs() const {
        return _xs;
    }

    bool contains_point(const X& x, const Y& y) const {
        int xi = x_index(x);
        if (xi == -1) return false;
        return y_index(xi + _size, y) != -1;
    }

    void set(const X& x, const Y& y, T value) {
        int xi = x_index(x);
        assert(xi != -1);
        assert(y_index(xi + _size, y) != -1);

        int k = xi + _size;
        set_exact(k, y, std::move(value));

        while (1 < k) {
            k >>= 1;
            set_exact(k, y, Monoid::op(get_exact(2 * k, y), get_exact(2 * k + 1, y)));
        }
    }

    T get(const X& x, const Y& y) const {
        int xi = x_index(x);
        if (xi == -1) return Monoid::id();
        return get_exact(xi + _size, y);
    }

    T operator()(const X& x, const Y& y) const {
        return get(x, y);
    }

    T prod(const X& xl, const X& xr, const Y& yl, const Y& yr) const {
        assert(xl <= xr);
        assert(yl <= yr);

        if (xl == xr || yl == yr || empty()) return Monoid::id();

        int l = int(std::lower_bound(_xs.begin(), _xs.end(), xl) - _xs.begin());
        int r = int(std::lower_bound(_xs.begin(), _xs.end(), xr) - _xs.begin());

        l += _size;
        r += _size;

        T sml = Monoid::id();
        T smr = Monoid::id();

        while (l < r) {
            if (l & 1) sml = Monoid::op(sml, prod_y(l++, yl, yr));
            if (r & 1) smr = Monoid::op(prod_y(--r, yl, yr), smr);
            l >>= 1;
            r >>= 1;
        }

        return Monoid::op(sml, smr);
    }

    T all_prod() const {
        if (empty() || _d[1].empty()) return Monoid::id();
        return _d[1][1];
    }

    std::vector<weighted_point_type> to_vector() const {
        std::vector<weighted_point_type> res;
        res.reserve(_point_count);

        for (int xi = 0; xi < _n; xi++) {
            int k = xi + _size;
            int m = int(_ys[k].size());

            for (int j = 0; j < m; j++) {
                res.emplace_back(_xs[xi], _ys[k][j], _d[k][m + j]);
            }
        }

        return res;
    }
};

} // namespace ds
} // namespace m1une


#line 1 "monoid/add.hpp"



namespace m1une {
namespace monoid {

// Monoid for addition (Range Sum).
template <typename T>
struct Add {
    using value_type = T;
    static constexpr bool commutative = true;

    // Returns the identity element for addition, which is 0.
    static constexpr T id() {
        return T(0);
    }

    // Returns the sum of a and b.
    static constexpr T op(const T& a, const T& b) {
        return a + b;
    }

    static constexpr T inv(const T& x) {
        return -x;
    }
};

}  // namespace monoid
}  // namespace m1une


#line 5 "verify/ds/segtree/segtree_2d.test.cpp"

#line 8 "verify/ds/segtree/segtree_2d.test.cpp"
#include <cstdint>
#line 1 "utilities/fast_io.hpp"



#line 5 "utilities/fast_io.hpp"
#include <array>
#include <cerrno>
#include <charconv>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#line 12 "utilities/fast_io.hpp"
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#include <type_traits>
#line 18 "utilities/fast_io.hpp"
#include <unistd.h>
#line 20 "utilities/fast_io.hpp"

namespace m1une {
namespace utilities {

struct FastOutput;

namespace internal {

// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;

// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};

template <class T>
struct is_range<T, std::void_t<
    decltype(std::begin(std::declval<T&>())),
    decltype(std::end(std::declval<T&>()))
>> : std::true_type {};

template <class T>
inline constexpr bool is_range_v = is_range<T>::value;

template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));

template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;

template <class T, class = void>
struct range_stored_value {
    using type = range_value_t<T>;
};

template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
    using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};

template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;

// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};

template <class T, std::size_t N>
struct is_char_array<T[N]>
    : std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};

template <class T>
struct is_string_like
    : std::bool_constant<
          std::is_same_v<std::decay_t<T>, std::string>
          || std::is_same_v<std::decay_t<T>, const char*>
          || std::is_same_v<std::decay_t<T>, char*>
          || is_char_array<std::remove_reference_t<T>>::value
      > {};

template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;

// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};

template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
    : std::true_type {};

template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;

template <class T, class = void>
struct has_static_mod_raw : std::false_type {};

template <class T>
struct has_static_mod_raw<
    T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
    : std::true_type {};

template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;

// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
    std::is_integral_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>
    || std::is_same_v<std::remove_cv_t<T>, __uint128_t>;

template <class T>
inline constexpr bool is_signed_v =
    std::is_signed_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>;

template <class T>
struct make_unsigned {
    using type = std::make_unsigned_t<T>;
};

template <>
struct make_unsigned<__int128_t> {
    using type = __uint128_t;
};

template <>
struct make_unsigned<__uint128_t> {
    using type = __uint128_t;
};

template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;

}  // namespace internal

struct FastInput {
    static constexpr int buffer_size = 1 << 20;

   private:
    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _length;
    int _file_descriptor;
    bool _streaming;

    bool refill() {
        _position = 0;
        if (_streaming) {
            ssize_t length;
            do {
                length = ::read(_file_descriptor, _buffer, buffer_size);
            } while (length < 0 && errno == EINTR);
            if (length <= 0) {
                _length = 0;
                return false;
            }
            _length = int(length);
        } else {
            _length = int(std::fread(_buffer, 1, buffer_size, _stream));
        }
        return _length != 0;
    }

    template <class T>
    bool read_integer_from_stream(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = read_char_raw();
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = negative ? result * 10 - (c - '0')
                                  : result * 10 + (c - '0');
                c = read_char_raw();
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = result * 10 + T(c - '0');
                c = read_char_raw();
            }
            value = negative ? T(0) - result : result;
        }
        return true;
    }

    bool prepare_number() {
        if (_length - _position >= 64) return true;
        const int remaining = _length - _position;
        if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
        const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
        _position = 0;
        _length = remaining + added;
        if (_length < buffer_size) _buffer[_length] = '\0';
        return _length != 0;
    }

   public:
    explicit FastInput(std::FILE* stream = stdin)
        : _stream(stream),
          _position(0),
          _length(0),
          _file_descriptor(::fileno(stream)),
          _streaming([&] {
              struct stat status;
              return _file_descriptor >= 0
                     && ::fstat(_file_descriptor, &status) == 0
                     && !S_ISREG(status.st_mode);
          }()) {}

    FastInput(const FastInput&) = delete;
    FastInput& operator=(const FastInput&) = delete;

    int read_char_raw() {
        if (_position == _length && !refill()) return EOF;
        return _buffer[_position++];
    }

    bool skip_spaces() {
        int c = read_char_raw();
        while (c != EOF && c <= ' ') c = read_char_raw();
        if (c == EOF) return false;
        --_position;
        return true;
    }

    bool read(char& value) {
        if (!skip_spaces()) return false;
        value = char(read_char_raw());
        return true;
    }

    bool read(std::string& value) {
        if (!skip_spaces()) return false;
        value.clear();
        while (true) {
            const int begin = _position;
            while (_position < _length &&
                   static_cast<unsigned char>(_buffer[_position]) > ' ') {
                ++_position;
            }
            value.append(_buffer + begin, _position - begin);
            if (_position < _length) {
                ++_position;
                return true;
            }
            if (!refill()) return true;
        }
    }

    bool read(bool& value) {
        int x;
        if (!read(x)) return false;
        value = x != 0;
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>,
        bool
    >
    read(T& value) {
        if (_streaming) return read_integer_from_stream(value);
        if (!prepare_number()) return false;
        int c = static_cast<unsigned char>(_buffer[_position++]);
        while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = static_cast<unsigned char>(_buffer[_position++]);
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const int first = c - '0';
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = negative ? result * 100 - (first * 10 + second)
                                      : result * 100 + (first * 10 + second);
                    ++_position;
                } else {
                    result = negative ? result * 10 - first : result * 10 + first;
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const unsigned first = unsigned(c - '0');
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = result * 100 + T(first * 10 + unsigned(second));
                    ++_position;
                } else {
                    result = result * 10 + T(first);
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = negative ? T(0) - result : result;
        }
        if (_position > _length) _position = _length;
        return true;
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>, bool>
    read(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();
        bool negative = false;
        if (c == '-' || c == '+') {
            negative = c == '-';
            c = read_char_raw();
        }

        long double result = 0;
        while ('0' <= c && c <= '9') {
            result = result * 10 + (c - '0');
            c = read_char_raw();
        }
        if (c == '.') {
            long double place = 0.1L;
            c = read_char_raw();
            while ('0' <= c && c <= '9') {
                result += (c - '0') * place;
                place *= 0.1L;
                c = read_char_raw();
            }
        }
        if (c == 'e' || c == 'E') {
            c = read_char_raw();
            bool exponent_negative = false;
            if (c == '-' || c == '+') {
                exponent_negative = c == '-';
                c = read_char_raw();
            }
            int exponent = 0;
            while ('0' <= c && c <= '9') {
                exponent = exponent * 10 + (c - '0');
                c = read_char_raw();
            }
            long double scale = 1;
            long double power = 10;
            while (exponent > 0) {
                if (exponent & 1) scale *= power;
                power *= power;
                exponent >>= 1;
            }
            result = exponent_negative ? result / scale : result * scale;
        }
        value = static_cast<T>(negative ? -result : result);
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>,
        bool
    >
    read(T& value) {
        long long x;
        if (!read(x)) return false;
        if constexpr (internal::has_static_mod_raw_v<T>) {
            if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
                value = T::raw(uint32_t(x));
            } else {
                value = T(x);
            }
        } else {
            value = T(x);
        }
        return true;
    }

    template <class First, class Second>
    bool read(std::pair<First, Second>& value) {
        if (!read(value.first)) return false;
        return read(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>,
        bool
    >
    read(Range& range) {
        using StoredValue = internal::range_stored_value_t<Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        for (auto&& value : range) {
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                bool x;
                if (!read(x)) return false;
                value = x;
            } else {
                if (!read(value)) return false;
            }
        }
        return true;
    }

    template <class First, class Second, class... Rest>
    bool read(First& first, Second& second, Rest&... rest) {
        if (!read(first)) return false;
        return read(second, rest...);
    }

    template <class T>
    FastInput& operator>>(T& value) {
        if (!read(value)) std::abort();
        return *this;
    }
};

struct FastOutput {
    static constexpr int buffer_size = 1 << 20;

   private:
    inline static const auto digit_quads = [] {
        std::array<char, 40000> result{};
        for (int i = 0; i < 10000; i++) {
            int value = i;
            for (int j = 3; j >= 0; j--) {
                result[4 * i + j] = char('0' + value % 10);
                value /= 10;
            }
        }
        return result;
    }();

    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _precision;
    std::chars_format _float_format;
    char _range_separator;
    std::string* _capture = nullptr;

    template <class T>
    std::string format_cell(const T& value) {
        std::string result;
        struct CaptureGuard {
            std::string*& target;
            std::string* previous;
            ~CaptureGuard() { target = previous; }
        } guard{_capture, _capture};
        _capture = &result;
        write(value);
        return result;
    }

    template <class Matrix>
    void write_aligned_matrix(const Matrix& matrix) {
        std::vector<std::vector<std::string>> rows;
        std::vector<std::size_t> widths;
        for (const auto& row : matrix) {
            auto& cells = rows.emplace_back();
            std::size_t column = 0;
            for (const auto& value : row) {
                cells.push_back(format_cell(value));
                if (column == widths.size()) widths.push_back(0);
                widths[column] = std::max(widths[column], cells.back().size());
                ++column;
            }
        }
        bool first = true;
        for (const auto& row : rows) {
            if (!first) write_char('\n');
            first = false;
            for (std::size_t column = 0; column < row.size(); ++column) {
                if (column != 0) write_char(_range_separator);
                for (std::size_t padding = row[column].size();
                     padding < widths[column]; ++padding) {
                    write_char(' ');
                }
                write(row[column]);
            }
        }
    }

   public:
    explicit FastOutput(std::FILE* stream = stdout)
        : _stream(stream),
          _position(0),
          _precision(6),
          _float_format(std::chars_format::general),
          _range_separator(' ') {
        if (_stream == stdout
            && internal::standard_output_instance == nullptr) {
            internal::standard_output_instance = this;
        }
    }

    FastOutput(const FastOutput&) = delete;
    FastOutput& operator=(const FastOutput&) = delete;

    ~FastOutput() {
        flush();
        if (internal::standard_output_instance == this) {
            internal::standard_output_instance = nullptr;
        }
    }

    void flush() {
        if (_position != 0) {
            std::fwrite(_buffer, 1, _position, _stream);
            _position = 0;
        }
        std::fflush(_stream);
    }

    void write_char(char c) {
        if (_capture != nullptr) {
            _capture->push_back(c);
            return;
        }
        if (_position == buffer_size) flush();
        _buffer[_position++] = c;
    }

    void write(const char* s) {
        while (*s != '\0') write_char(*s++);
    }

    void write(const std::string& s) {
        if (_capture != nullptr) {
            _capture->append(s);
            return;
        }
        std::size_t position = 0;
        while (position < s.size()) {
            if (_position == buffer_size) flush();
            const std::size_t copied =
                std::min<std::size_t>(buffer_size - _position, s.size() - position);
            std::memcpy(_buffer + _position, s.data() + position, copied);
            _position += int(copied);
            position += copied;
        }
    }

    void write(char c) {
        write_char(c);
    }

    void write(bool value) {
        write_char(value ? '1' : '0');
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>>
    write(T value) {
        char digits[128];
        auto [end, error] = std::to_chars(
            digits,
            digits + sizeof(digits),
            value,
            _float_format,
            _precision
        );
        if (error != std::errc()) std::abort();
        for (const char* pointer = digits; pointer != end; pointer++) {
            write_char(*pointer);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>
    >
    write(T value) {
        using Raw = std::remove_cv_t<T>;
        using Unsigned = internal::make_unsigned_t<Raw>;

        Unsigned magnitude;
        if constexpr (internal::is_signed_v<Raw>) {
            if (value < 0) {
                write_char('-');
                magnitude = Unsigned(0) - Unsigned(value);
            } else {
                magnitude = Unsigned(value);
            }
        } else {
            magnitude = value;
        }

        if (magnitude == 0) {
            write_char('0');
            return;
        }

        unsigned chunks[16];
        int count = 0;
        while (magnitude >= 10000) {
            const Unsigned quotient = magnitude / 10000;
            chunks[count++] = unsigned(magnitude - quotient * 10000);
            magnitude = quotient;
        }
        if (_capture == nullptr && _position > buffer_size - 64) flush();
        char captured[64];
        char* const begin = _capture != nullptr ? captured : _buffer + _position;
        char* destination = begin;
        const unsigned leading = unsigned(magnitude);
        const char* first = digit_quads.data() + 4 * leading;
        int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
        for (; skip < 4; skip++) *destination++ = first[skip];
        while (count--) {
            const char* digits = digit_quads.data() + 4 * chunks[count];
            std::memcpy(destination, digits, 4);
            destination += 4;
        }
        if (_capture != nullptr) {
            _capture->append(begin, destination - begin);
        } else {
            _position += int(destination - begin);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>
    >
    write(const T& value) {
        write(value.val());
    }

    template <class First, class Second>
    void write(const std::pair<First, Second>& value) {
        write(value.first);
        write_char(' ');
        write(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>
    >
    write(const Range& range) {
        using StoredValue = internal::range_stored_value_t<const Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        bool first = true;
        for (const auto& value : range) {
            if (!first) write_char(nested ? '\n' : _range_separator);
            first = false;
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                write(static_cast<bool>(value));
            } else {
                write(value);
            }
        }
    }

    template <class First, class... Rest>
    void print(const First& first, const Rest&... rest) {
        write(first);
        ((write_char(' '), write(rest)), ...);
    }

    void println() {
        write_char('\n');
    }

    void set_precision(int precision) {
        _precision = precision;
    }

    void set_fixed(int precision = 6) {
        _float_format = std::chars_format::fixed;
        _precision = precision;
    }

    void set_general(int precision = 6) {
        _float_format = std::chars_format::general;
        _precision = precision;
    }

    void set_range_separator(char separator) {
        _range_separator = separator;
    }

    template <class Matrix>
    void write_aligned(const Matrix& matrix) {
        using Row = internal::range_stored_value_t<const Matrix>;
        using Cell = internal::range_stored_value_t<const Row>;
        static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
                      "write_aligned requires a two-dimensional range");
        static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
                      "write_aligned requires scalar cells");
        write_aligned_matrix(matrix);
    }

    template <class Matrix>
    void println_aligned(const Matrix& matrix) {
        write_aligned(matrix);
        write_char('\n');
    }

    template <class... Args>
    void println(const Args&... args) {
        print(args...);
        write_char('\n');
    }

    template <class T>
    FastOutput& operator<<(const T& value) {
        write(value);
        return *this;
    }
};

}  // namespace utilities
}  // namespace m1une


#line 10 "verify/ds/segtree/segtree_2d.test.cpp"
#include <map>
#include <random>
#line 15 "verify/ds/segtree/segtree_2d.test.cpp"

using Sum = m1une::monoid::Add<long long>;

struct Query {
    int type;
    int first;
    int second;
    int third;
    int fourth;
    long long value;
};

#ifndef NDEBUG
void randomized_test() {
    std::mt19937 random(314159265);
    std::vector<std::pair<int, int>> points;
    std::map<std::pair<int, int>, long long> expected;
    for (int i = 0; i < 40; i++) {
        int x = int(random() % 15) - 7;
        int y = int(random() % 15) - 7;
        points.emplace_back(x, y);
        expected[{x, y}] = 0;
    }

    m1une::ds::Segtree2D<Sum> seg(points);
    assert(seg.size() == int(expected.size()));
    assert(!seg.contains_point(100, 100));
    assert(seg.get(100, 100) == 0);

    std::vector<std::pair<int, int>> distinct_points;
    for (const auto& [point, value] : expected) {
        (void)value;
        distinct_points.push_back(point);
    }

    for (int operation = 0; operation < 1000; operation++) {
        if (random() % 3 == 0) {
            auto point = distinct_points[random() % distinct_points.size()];
            long long value = int(random() % 101) - 50;
            seg.set(point.first, point.second, value);
            expected[point] = value;
            assert(seg(point.first, point.second) == value);
        } else {
            int x_lower = int(random() % 19) - 9;
            int x_upper = int(random() % 19) - 9;
            int y_lower = int(random() % 19) - 9;
            int y_upper = int(random() % 19) - 9;
            if (x_upper < x_lower) std::swap(x_lower, x_upper);
            if (y_upper < y_lower) std::swap(y_lower, y_upper);

            long long answer = 0;
            for (const auto& [point, value] : expected) {
                if (x_lower <= point.first && point.first < x_upper &&
                    y_lower <= point.second && point.second < y_upper) {
                    answer += value;
                }
            }
            assert(seg.prod(x_lower, x_upper, y_lower, y_upper) == answer);
        }
    }

    long long total = 0;
    for (const auto& [point, value] : expected) {
        (void)point;
        total += value;
    }
    assert(seg.all_prod() == total);
    auto values = seg.to_vector();
    assert(values.size() == expected.size());
    for (const auto& [x, y, value] : values) {
        std::pair<int, int> point(x, y);
        assert(expected[point] == value);
    }
}
#endif

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

#ifndef NDEBUG
    randomized_test();
#endif

    int n, q;
    fast_input >> n >> q;
    std::vector<std::tuple<int, int, long long>> initial(n);
    std::vector<std::pair<int, int>> points;
    points.reserve(n + q);
    for (auto& [x, y, weight] : initial) {
        fast_input >> x >> y >> weight;
        points.emplace_back(x, y);
    }

    std::vector<Query> queries(q);
    for (Query& query : queries) {
        fast_input >> query.type;
        if (query.type == 0) {
            fast_input >> query.first >> query.second >> query.value;
            query.third = query.fourth = 0;
            points.emplace_back(query.first, query.second);
        } else {
            fast_input >> query.first >> query.second >> query.third >> query.fourth;
            query.value = 0;
        }
    }

    m1une::ds::Segtree2D<Sum> seg(std::move(points));
    for (const auto& [x, y, weight] : initial) {
        seg.set(x, y, seg.get(x, y) + weight);
    }

    for (const Query& query : queries) {
        if (query.type == 0) {
            long long current = seg.get(query.first, query.second);
            seg.set(query.first, query.second, current + query.value);
        } else {
            fast_output << seg.prod(query.first, query.third, query.second, query.fourth)
                      << '\n';
        }
    }
}

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