C++ Library for Competitive Programming
/*
* @title データ構造/セグメント木
*
* verification-helper: PROBLEM https://judge.yosupo.jp/problem/point_set_range_composite
*/
#include <iostream>
#include <utility>
#include <vector>
#include "emthrm/data_structure/segment_tree.hpp"
#include "emthrm/math/modint.hpp"
int main() {
using ModInt = emthrm::MInt<998244353>;
int n, q;
std::cin >> n >> q;
struct M {
using Monoid = std::pair<ModInt, ModInt>;
static constexpr Monoid id() { return {1, 0}; }
static Monoid merge(const Monoid& a, const Monoid& b) {
return {a.first * b.first, a.second * b.first + b.second};
}
};
std::vector<M::Monoid> f(n);
for (int i = 0; i < n; ++i) {
std::cin >> f[i].first >> f[i].second;
}
emthrm::SegmentTree<M> seg(f);
while (q--) {
int query;
std::cin >> query;
if (query == 0) {
int p, c, d;
std::cin >> p >> c >> d;
seg.set(p, {c, d});
} else if (query == 1) {
int l, r, x;
std::cin >> l >> r >> x;
const M::Monoid ans = seg.get(l, r);
std::cout << ans.first * x + ans.second << '\n';
}
}
return 0;
}
#line 1 "test/data_structure/segment_tree.test.cpp"
/*
* @title データ構造/セグメント木
*
* verification-helper: PROBLEM https://judge.yosupo.jp/problem/point_set_range_composite
*/
#include <iostream>
#include <utility>
#include <vector>
#line 1 "include/emthrm/data_structure/segment_tree.hpp"
#include <algorithm>
#include <bit>
#include <limits>
#include <type_traits>
#line 9 "include/emthrm/data_structure/segment_tree.hpp"
namespace emthrm {
template <typename T>
requires requires {
typename T::Monoid;
{T::id()} -> std::same_as<typename T::Monoid>;
{T::merge(std::declval<typename T::Monoid>(),
std::declval<typename T::Monoid>())}
-> std::same_as<typename T::Monoid>;
}
struct SegmentTree {
using Monoid = typename T::Monoid;
explicit SegmentTree(const int n)
: SegmentTree(std::vector<Monoid>(n, T::id())) {}
explicit SegmentTree(const std::vector<Monoid>& a)
: n(a.size()), p2(std::bit_ceil(a.size())) {
dat.assign(p2 << 1, T::id());
std::copy(a.begin(), a.end(), dat.begin() + p2);
for (int i = p2 - 1; i > 0; --i) {
dat[i] = T::merge(dat[i << 1], dat[(i << 1) + 1]);
}
}
void set(int idx, const Monoid val) {
idx += p2;
dat[idx] = val;
while (idx >>= 1) dat[idx] = T::merge(dat[idx << 1], dat[(idx << 1) + 1]);
}
Monoid get(int left, int right) const {
Monoid res_l = T::id(), res_r = T::id();
for (left += p2, right += p2; left < right; left >>= 1, right >>= 1) {
if (left & 1) res_l = T::merge(res_l, dat[left++]);
if (right & 1) res_r = T::merge(dat[--right], res_r);
}
return T::merge(res_l, res_r);
}
Monoid operator[](const int idx) const { return dat[idx + p2]; }
template <typename G>
int find_right(int left, const G g) const {
if (left >= n) [[unlikely]] return n;
Monoid val = T::id();
left += p2;
do {
while (!(left & 1)) left >>= 1;
Monoid nxt = T::merge(val, dat[left]);
if (!g(nxt)) {
while (left < p2) {
left <<= 1;
nxt = T::merge(val, dat[left]);
if (g(nxt)) {
val = nxt;
++left;
}
}
return left - p2;
}
val = nxt;
++left;
} while (!std::has_single_bit(static_cast<unsigned int>(left)));
return n;
}
template <typename G>
int find_left(int right, const G g) const {
if (right <= 0) [[unlikely]] return -1;
Monoid val = T::id();
right += p2;
do {
--right;
while (right > 1 && (right & 1)) right >>= 1;
Monoid nxt = T::merge(dat[right], val);
if (!g(nxt)) {
while (right < p2) {
right = (right << 1) + 1;
nxt = T::merge(dat[right], val);
if (g(nxt)) {
val = nxt;
--right;
}
}
return right - p2;
}
val = nxt;
} while (!std::has_single_bit(static_cast<unsigned int>(right)));
return -1;
}
private:
const int n, p2;
std::vector<Monoid> dat;
};
namespace monoid {
template <typename T>
struct RangeMinimumQuery {
using Monoid = T;
static constexpr Monoid id() { return std::numeric_limits<Monoid>::max(); }
static Monoid merge(const Monoid& a, const Monoid& b) {
return std::min(a, b);
}
};
template <typename T>
struct RangeMaximumQuery {
using Monoid = T;
static constexpr Monoid id() { return std::numeric_limits<Monoid>::lowest(); }
static Monoid merge(const Monoid& a, const Monoid& b) {
return std::max(a, b);
}
};
template <typename T>
struct RangeSumQuery {
using Monoid = T;
static constexpr Monoid id() { return 0; }
static Monoid merge(const Monoid& a, const Monoid& b) { return a + b; }
};
} // namespace monoid
} // namespace emthrm
#line 1 "include/emthrm/math/modint.hpp"
#ifndef ARBITRARY_MODINT
# include <cassert>
#endif
#include <compare>
#line 9 "include/emthrm/math/modint.hpp"
// #include <numeric>
#line 12 "include/emthrm/math/modint.hpp"
namespace emthrm {
#ifndef ARBITRARY_MODINT
template <unsigned int M>
struct MInt {
unsigned int v;
constexpr MInt() : v(0) {}
constexpr MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}
static constexpr MInt raw(const int x) {
MInt x_;
x_.v = x;
return x_;
}
static constexpr int get_mod() { return M; }
static constexpr void set_mod(const int divisor) {
assert(std::cmp_equal(divisor, M));
}
static void init(const int x) {
inv<true>(x);
fact(x);
fact_inv(x);
}
template <bool MEMOIZES = false>
static MInt inv(const int n) {
// assert(0 <= n && n < M && std::gcd(n, M) == 1);
static std::vector<MInt> inverse{0, 1};
const int prev = inverse.size();
if (n < prev) return inverse[n];
if constexpr (MEMOIZES) {
// "n!" and "M" must be disjoint.
inverse.resize(n + 1);
for (int i = prev; i <= n; ++i) {
inverse[i] = -inverse[M % i] * raw(M / i);
}
return inverse[n];
}
int u = 1, v = 0;
for (unsigned int a = n, b = M; b;) {
const unsigned int q = a / b;
std::swap(a -= q * b, b);
std::swap(u -= q * v, v);
}
return u;
}
static MInt fact(const int n) {
static std::vector<MInt> factorial{1};
if (const int prev = factorial.size(); n >= prev) {
factorial.resize(n + 1);
for (int i = prev; i <= n; ++i) {
factorial[i] = factorial[i - 1] * i;
}
}
return factorial[n];
}
static MInt fact_inv(const int n) {
static std::vector<MInt> f_inv{1};
if (const int prev = f_inv.size(); n >= prev) {
f_inv.resize(n + 1);
f_inv[n] = inv(fact(n).v);
for (int i = n; i > prev; --i) {
f_inv[i - 1] = f_inv[i] * i;
}
}
return f_inv[n];
}
static MInt nCk(const int n, const int k) {
if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
fact_inv(n - k) * fact_inv(k));
}
static MInt nPk(const int n, const int k) {
return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k);
}
static MInt nHk(const int n, const int k) {
return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k));
}
static MInt large_nCk(long long n, const int k) {
if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
inv<true>(k);
MInt res = 1;
for (int i = 1; i <= k; ++i) {
res *= inv(i) * n--;
}
return res;
}
constexpr MInt pow(long long exponent) const {
MInt res = 1, tmp = *this;
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
}
return res;
}
constexpr MInt& operator+=(const MInt& x) {
if ((v += x.v) >= M) v -= M;
return *this;
}
constexpr MInt& operator-=(const MInt& x) {
if ((v += M - x.v) >= M) v -= M;
return *this;
}
constexpr MInt& operator*=(const MInt& x) {
v = (unsigned long long){v} * x.v % M;
return *this;
}
MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }
constexpr auto operator<=>(const MInt& x) const = default;
constexpr MInt& operator++() {
if (++v == M) [[unlikely]] v = 0;
return *this;
}
constexpr MInt operator++(int) {
const MInt res = *this;
++*this;
return res;
}
constexpr MInt& operator--() {
v = (v == 0 ? M - 1 : v - 1);
return *this;
}
constexpr MInt operator--(int) {
const MInt res = *this;
--*this;
return res;
}
constexpr MInt operator+() const { return *this; }
constexpr MInt operator-() const { return raw(v ? M - v : 0); }
constexpr MInt operator+(const MInt& x) const { return MInt(*this) += x; }
constexpr MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
constexpr MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
MInt operator/(const MInt& x) const { return MInt(*this) /= x; }
friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
return os << x.v;
}
friend std::istream& operator>>(std::istream& is, MInt& x) {
long long v;
is >> v;
x = MInt(v);
return is;
}
};
#else // ARBITRARY_MODINT
template <int ID>
struct MInt {
unsigned int v;
constexpr MInt() : v(0) {}
MInt(const long long x) : v(x >= 0 ? x % mod() : x % mod() + mod()) {}
static constexpr MInt raw(const int x) {
MInt x_;
x_.v = x;
return x_;
}
static int get_mod() { return mod(); }
static void set_mod(const unsigned int divisor) { mod() = divisor; }
static void init(const int x) {
inv<true>(x);
fact(x);
fact_inv(x);
}
template <bool MEMOIZES = false>
static MInt inv(const int n) {
// assert(0 <= n && n < mod() && std::gcd(x, mod()) == 1);
static std::vector<MInt> inverse{0, 1};
const int prev = inverse.size();
if (n < prev) return inverse[n];
if constexpr (MEMOIZES) {
// "n!" and "M" must be disjoint.
inverse.resize(n + 1);
for (int i = prev; i <= n; ++i) {
inverse[i] = -inverse[mod() % i] * raw(mod() / i);
}
return inverse[n];
}
int u = 1, v = 0;
for (unsigned int a = n, b = mod(); b;) {
const unsigned int q = a / b;
std::swap(a -= q * b, b);
std::swap(u -= q * v, v);
}
return u;
}
static MInt fact(const int n) {
static std::vector<MInt> factorial{1};
if (const int prev = factorial.size(); n >= prev) {
factorial.resize(n + 1);
for (int i = prev; i <= n; ++i) {
factorial[i] = factorial[i - 1] * i;
}
}
return factorial[n];
}
static MInt fact_inv(const int n) {
static std::vector<MInt> f_inv{1};
if (const int prev = f_inv.size(); n >= prev) {
f_inv.resize(n + 1);
f_inv[n] = inv(fact(n).v);
for (int i = n; i > prev; --i) {
f_inv[i - 1] = f_inv[i] * i;
}
}
return f_inv[n];
}
static MInt nCk(const int n, const int k) {
if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
fact_inv(n - k) * fact_inv(k));
}
static MInt nPk(const int n, const int k) {
return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k);
}
static MInt nHk(const int n, const int k) {
return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k));
}
static MInt large_nCk(long long n, const int k) {
if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
inv<true>(k);
MInt res = 1;
for (int i = 1; i <= k; ++i) {
res *= inv(i) * n--;
}
return res;
}
MInt pow(long long exponent) const {
MInt res = 1, tmp = *this;
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
}
return res;
}
MInt& operator+=(const MInt& x) {
if ((v += x.v) >= mod()) v -= mod();
return *this;
}
MInt& operator-=(const MInt& x) {
if ((v += mod() - x.v) >= mod()) v -= mod();
return *this;
}
MInt& operator*=(const MInt& x) {
v = (unsigned long long){v} * x.v % mod();
return *this;
}
MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }
auto operator<=>(const MInt& x) const = default;
MInt& operator++() {
if (++v == mod()) [[unlikely]] v = 0;
return *this;
}
MInt operator++(int) {
const MInt res = *this;
++*this;
return res;
}
MInt& operator--() {
v = (v == 0 ? mod() - 1 : v - 1);
return *this;
}
MInt operator--(int) {
const MInt res = *this;
--*this;
return res;
}
MInt operator+() const { return *this; }
MInt operator-() const { return raw(v ? mod() - v : 0); }
MInt operator+(const MInt& x) const { return MInt(*this) += x; }
MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
MInt operator/(const MInt& x) const { return MInt(*this) /= x; }
friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
return os << x.v;
}
friend std::istream& operator>>(std::istream& is, MInt& x) {
long long v;
is >> v;
x = MInt(v);
return is;
}
private:
static unsigned int& mod() {
static unsigned int divisor = 0;
return divisor;
}
};
#endif // ARBITRARY_MODINT
} // namespace emthrm
#line 13 "test/data_structure/segment_tree.test.cpp"
int main() {
using ModInt = emthrm::MInt<998244353>;
int n, q;
std::cin >> n >> q;
struct M {
using Monoid = std::pair<ModInt, ModInt>;
static constexpr Monoid id() { return {1, 0}; }
static Monoid merge(const Monoid& a, const Monoid& b) {
return {a.first * b.first, a.second * b.first + b.second};
}
};
std::vector<M::Monoid> f(n);
for (int i = 0; i < n; ++i) {
std::cin >> f[i].first >> f[i].second;
}
emthrm::SegmentTree<M> seg(f);
while (q--) {
int query;
std::cin >> query;
if (query == 0) {
int p, c, d;
std::cin >> p >> c >> d;
seg.set(p, {c, d});
} else if (query == 1) {
int l, r, x;
std::cin >> l >> r >> x;
const M::Monoid ans = seg.get(l, r);
std::cout << ans.first * x + ans.second << '\n';
}
}
return 0;
}