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:x: verify/unit_test/lazy_segtree.test.cpp

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Code

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

#include <iostream>

#include "data_structure/segtree/lazy_segtree.hpp"
#include "monoid/acted_monoids/range_affine_range_sum.hpp"

#include "atcoder/modint.hpp"

using namespace std;
using namespace m1une;

using mint = atcoder::modint998244353;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int N, Q;
    cin >> N >> Q;
    lazy_segment_tree<range_affine_range_sum_monoid<mint>> seg(N);
    for (int i = 0; i < N; i++) {
        int a;
        cin >> a;
        seg.set(i, {mint(a), 1});
    }
    while (Q--) {
        int t;
        cin >> t;
        if (t == 0) {
            int l, r, b, c;
            cin >> l >> r >> b >> c;
            seg.apply(l, r, {mint(b), mint(c)});
        } else {
            int l, r;
            cin >> l >> r;
            mint ans = seg.prod(l, r).value;
            cout << ans.val() << endl;
        }
    }
}
#line 1 "verify/unit_test/lazy_segtree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"

#include <iostream>

#line 1 "data_structure/segtree/lazy_segtree.hpp"



#include <algorithm>
#include <functional>
#include <type_traits>
#include <vector>

#line 1 "monoid/acted_monoid.hpp"



#include <concepts>
#line 7 "monoid/acted_monoid.hpp"

#line 1 "monoid/monoid.hpp"



#line 7 "monoid/monoid.hpp"

namespace m1une {

template <typename T, auto operation, auto identity, bool commutative>
struct monoid {
    static_assert(std::is_invocable_r_v<T, decltype(operation), T, T>, "operation must work as T(T, T)");
    static_assert(std::is_invocable_r_v<T, decltype(identity)>, "identity must work as T()");

    using value_type = T;
    static constexpr auto op = operation;
    static constexpr auto id = identity;
    static constexpr bool is_commutative = commutative;
};

template <typename T>
concept Monoid = requires(typename T::value_type v) {
    typename T::value_type;
    { T::op(v, v) } -> std::same_as<typename T::value_type>;
    { T::id() } -> std::same_as<typename T::value_type>;
    { T::is_commutative } -> std::convertible_to<bool>;
};

}  // namespace m1une


#line 9 "monoid/acted_monoid.hpp"

namespace m1une {

template <Monoid Data, Monoid Act, auto mapping>
struct acted_monoid {
    using data_monoid = Data;
    using act_monoid = Act;

    using data_type = typename Data::value_type;
    using act_type = typename Act::value_type;

    static_assert(std::is_invocable_r_v<data_type, decltype(mapping), act_type, data_type>,
                  "mapping must work as data_type(act_type, data_type)");

    static constexpr auto data_op = Data::op;
    static constexpr auto data_id = Data::id;
    static constexpr bool data_is_commutative = Data::is_commutative;
    static constexpr auto act_op = Act::op;
    static constexpr auto act_id = Act::id;
    static constexpr bool act_is_commutative = Act::is_commutative;
    static constexpr auto apply = mapping;
};

template <typename T>
concept ActedMonoid = requires(typename T::data_type d, typename T::act_type a) {
    typename T::data_monoid;
    typename T::act_monoid;
    typename T::data_type;
    typename T::act_type;
    requires Monoid<typename T::data_monoid>;
    requires Monoid<typename T::act_monoid>;
    { T::apply(a, d) } -> std::same_as<typename T::data_type>;
};

}  // namespace m1une


#line 1 "utilities/bit_ceil.hpp"



namespace m1une {
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 m1une


#line 11 "data_structure/segtree/lazy_segtree.hpp"

namespace m1une {

template <ActedMonoid AM>
struct lazy_segment_tree {
    using S = typename AM::data_type;
    using F = typename AM::act_type;

   private:
    int _n;
    int _size;
    int _log;
    std::vector<S> _data;
    std::vector<F> _lazy;

    void update(int k) {
        _data[k] = AM::data_op(_data[2 * k], _data[2 * k + 1]);
    }

    void all_apply(int k, F f) {
        _data[k] = AM::apply(f, _data[k]);
        if (k < _size) {
            _lazy[k] = AM::act_op(_lazy[k], f);
        }
    }

    void push(int k) {
        all_apply(2 * k, _lazy[k]);
        all_apply(2 * k + 1, _lazy[k]);
        _lazy[k] = AM::act_id();
    }

   public:
    lazy_segment_tree() : lazy_segment_tree(0) {}
    explicit lazy_segment_tree(int n) : lazy_segment_tree(std::vector<S>(n, AM::data_id())) {}
    explicit lazy_segment_tree(const std::vector<S>& v) : _n(v.size()) {
        _size = bit_ceil((unsigned int)_n);
        _log = 0;
        while ((1U << _log) < (unsigned int)_size) _log++;
        _data.assign(2 * _size, AM::data_id());
        _lazy.assign(_size, AM::act_id());
        for (int i = 0; i < _n; i++) {
            _data[_size + i] = v[i];
        }
        for (int i = _size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        p += _size;
        for (int i = _log; i >= 1; i--) push(p >> i);
        _data[p] = x;
        for (int i = 1; i <= _log; i++) update(p >> i);
    }

    S get(int p) {
        p += _size;
        for (int i = _log; i >= 1; i--) push(p >> i);
        return _data[p];
    }

    S prod(int l, int r) {
        if (l == r) return AM::data_id();

        l += _size;
        r += _size;

        for (int i = _log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        S sml = AM::data_id(), smr = AM::data_id();
        while (l < r) {
            if (l & 1) sml = AM::data_op(sml, _data[l++]);
            if (r & 1) smr = AM::data_op(_data[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return AM::data_op(sml, smr);
    }

    S all_prod() {
        return _data[1];
    }

    void apply(int p, F f) {
        p += _size;
        for (int i = _log; i >= 1; i--) push(p >> i);
        _data[p] = AM::apply(f, _data[p]);
        for (int i = 1; i <= _log; i++) update(p >> i);
    }

    void apply(int l, int r, F f) {
        if (l == r) return;

        l += _size;
        r += _size;

        for (int i = _log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for (int i = 1; i <= _log; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }

    int max_right(int l, auto g) {
        if (l == _n) return _n;
        l += _size;
        for (int i = _log; i >= 1; i--) push(l >> i);
        S sm = AM::data_id();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!g(AM::data_op(sm, _data[l]))) {
                while (l < _size) {
                    push(l);
                    l = (2 * l);
                    if (g(AM::data_op(sm, _data[l]))) {
                        sm = AM::data_op(sm, _data[l]);
                        l++;
                    }
                }
                return l - _size;
            }
            sm = AM::data_op(sm, _data[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    int min_left(int r, auto g) {
        if (r == 0) return 0;
        r += _size;
        for (int i = _log; i >= 1; i--) push((r - 1) >> i);
        S sm = AM::data_id();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!g(AM::data_op(_data[r], sm))) {
                while (r < _size) {
                    push(r);
                    r = (2 * r + 1);
                    if (g(AM::data_op(_data[r], sm))) {
                        sm = AM::data_op(_data[r], sm);
                        r--;
                    }
                }
                return r + 1 - _size;
            }
            sm = AM::data_op(_data[r], sm);
        } while ((r & -r) != r);
        return 0;
    }
};

}  // namespace m1une


#line 1 "monoid/acted_monoids/range_affine_range_sum.hpp"



#line 1 "monoid/monoid_addsz.hpp"



#line 5 "monoid/monoid_addsz.hpp"

#line 7 "monoid/monoid_addsz.hpp"

namespace m1une {

template <typename T>
struct value_and_size {
    T value;
    int size;
};

template <Monoid M>
using monoid_addsz = monoid<value_and_size<typename M::value_type>,
                            [](value_and_size<typename M::value_type> a, value_and_size<typename M::value_type> b) {
                                return value_and_size<typename M::value_type>{M::op(a.value, b.value), a.size + b.size};
                            },
                            []() { return value_and_size<typename M::value_type>{M::id(), 0}; }, M::is_commutative>;

}  // namespace m1une


#line 1 "monoid/monoids/add_monoid.hpp"



#line 5 "monoid/monoids/add_monoid.hpp"

namespace m1une {

template <typename T>
using add_monoid = monoid<T, [](T a, T b) { return a + b; }, []() { return T(0); }, true>;

}  // namespace m1une


#line 1 "monoid/monoids/affine_monoid.hpp"



#include <utility>

#line 7 "monoid/monoids/affine_monoid.hpp"

namespace m1une {

// Affine transformation f(x) = ax + b is represented as (a, b)
// perform f first, then g
// op(f, g)(x) = g(f(x))
template <typename T>
using affine_monoid = monoid<std::pair<T, T>,
                             [](std::pair<T, T> f, std::pair<T, T> g) {
                                 return std::pair<T, T>(f.first * g.first, f.second * g.first + g.second);
                             },
                             []() { return std::pair<T, T>(1, 0); }, false>;

}  // namespace m1une


#line 8 "monoid/acted_monoids/range_affine_range_sum.hpp"

namespace m1une {

template <typename T>
using range_affine_range_sum_monoid =
    acted_monoid<monoid_addsz<add_monoid<T>>, affine_monoid<T>,
                 [](typename affine_monoid<T>::value_type f, typename monoid_addsz<add_monoid<T>>::value_type x) {
                     // f = (a, b) is the affine transformation
                     // x = {value, size} is the data (sum and size of the range)
                     // Applying f to each element xi and summing up:
                     // sum(a*xi + b) = a * sum(xi) + b * size
                     return typename monoid_addsz<add_monoid<T>>::value_type{f.first * x.value + f.second * x.size,
                                                                             x.size};
                 }>;

}  // namespace m1une


#line 7 "verify/unit_test/lazy_segtree.test.cpp"

#line 1 "atcoder/modint.hpp"



#include <cassert>
#include <numeric>
#line 7 "atcoder/modint.hpp"

#ifdef _MSC_VER
#include <intrin.h>
#endif

#line 1 "atcoder/internal_math.hpp"



#line 5 "atcoder/internal_math.hpp"

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;

    // @param m `1 <= m`
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    // @return m
    unsigned int umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay

        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned long long y = x * _m;
        return (unsigned int)(z - y + (z < y ? _m : 0));
    }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        // y_max < m * (n + 1)
        // floor(y_max / m) <= n
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder


#line 1 "atcoder/internal_type_traits.hpp"



#line 7 "atcoder/internal_type_traits.hpp"

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder


#line 14 "atcoder/modint.hpp"

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }

    int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }

    int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder


#line 9 "verify/unit_test/lazy_segtree.test.cpp"

using namespace std;
using namespace m1une;

using mint = atcoder::modint998244353;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int N, Q;
    cin >> N >> Q;
    lazy_segment_tree<range_affine_range_sum_monoid<mint>> seg(N);
    for (int i = 0; i < N; i++) {
        int a;
        cin >> a;
        seg.set(i, {mint(a), 1});
    }
    while (Q--) {
        int t;
        cin >> t;
        if (t == 0) {
            int l, r, b, c;
            cin >> l >> r >> b >> c;
            seg.apply(l, r, {mint(b), mint(c)});
        } else {
            int l, r;
            cin >> l >> r;
            mint ans = seg.prod(l, r).value;
            cout << ans.val() << endl;
        }
    }
}
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