This documentation is automatically generated by online-judge-tools/verification-helper
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite"
#define FAST_IO
#include "../../template/template.hpp"
#include "../../number_theory/mod_int.hpp"
#include "../../data_structure/segment_tree.hpp"
using Mint = ModInt<mod998244353>;
struct Linear {
Mint a, b;
Linear() : a(Mint(1)), b(Mint(0)) {}
Linear(Mint _a, Mint _b) : a(_a), b(_b) {}
Mint operator()(Mint x) {
return a * x + b;
}
};
// f \circ g
Linear composite(const Linear &f, const Linear &g) {
return Linear(f.a * g.a, f.a * g.b + f.b);
}
struct Ops {
using Value = Linear;
static Value id() {
return Linear();
}
static Value op(const Value &x, const Value &y) {
return composite(y, x);
}
};
int main() {
i32 n, q;
cin >> n >> q;
Vec<Linear> fs(n);
REP(i, n) {
cin >> fs[i].a >> fs[i].b;
}
SegmentTree<Ops> seg(fs);
REP(qi, q) {
i32 type;
cin >> type;
if (type == 0) {
i32 p;
Linear f;
cin >> p >> f.a >> f.b;
seg.update(p, f);
} else {
i32 l, r;
Mint x;
cin >> l >> r >> x;
cout << seg.prod(l, r)(x) << '\n';
}
}
}#line 1 "data_structure/test/point_set_range_composite.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite"
#define FAST_IO
#line 1 "template/template.hpp"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i)
#define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using u128 = __uint128_t;
using i32 = signed int;
using i64 = signed long long;
using i128 = __int128_t;
using f64 = double;
using f80 = long double;
template <typename T>
using Vec = vector<T>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
return false;
}
istream &operator>>(istream &is, i128 &x) {
i64 v;
is >> v;
x = v;
return is;
}
ostream &operator<<(ostream &os, i128 x) {
os << (i64) x;
return os;
}
istream &operator>>(istream &is, u128 &x) {
u64 v;
is >> v;
x = v;
return is;
}
ostream &operator<<(ostream &os, u128 x) {
os << (u64) x;
return os;
}
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
SetUpIO() {
#ifdef FAST_IO
ios::sync_with_stdio(false);
cin.tie(nullptr);
#endif
cout << fixed << setprecision(15);
}
} set_up_io;
#line 2 "number_theory/mod_int.hpp"
#line 5 "number_theory/mod_int.hpp"
#include <type_traits>
#line 2 "number_theory/utils.hpp"
constexpr bool is_prime(unsigned n) {
if (n == 0 || n == 1) {
return false;
}
for (unsigned i = 2; i * i <= n; ++i) {
if (n % i == 0) {
return false;
}
}
return true;
}
constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
unsigned ret = 1, self = x;
while (y != 0) {
if (y & 1) {
ret = (unsigned) ((unsigned long long) ret * self % mod);
}
self = (unsigned) ((unsigned long long) self * self % mod);
y /= 2;
}
return ret;
}
template <unsigned mod>
constexpr unsigned primitive_root() {
static_assert(is_prime(mod), "`mod` must be a prime number.");
if (mod == 2) {
return 1;
}
unsigned primes[32] = {};
int it = 0;
{
unsigned m = mod - 1;
for (unsigned i = 2; i * i <= m; ++i) {
if (m % i == 0) {
primes[it++] = i;
while (m % i == 0) {
m /= i;
}
}
}
if (m != 1) {
primes[it++] = m;
}
}
for (unsigned i = 2; i < mod; ++i) {
bool ok = true;
for (int j = 0; j < it; ++j) {
if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
ok = false;
break;
}
}
if (ok)
return i;
}
return 0;
}
// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
x %= y;
if (x < 0) {
x += y;
}
return x;
}
// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return x / y;
} else {
return -((-x + y - 1) / y);
}
}
// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return (x + y - 1) / y;
} else {
return -(-x / y);
}
}
#line 8 "number_theory/mod_int.hpp"
template <unsigned mod>
class ModInt {
static_assert(mod != 0, "`mod` must not be equal to 0.");
static_assert(
mod < (1u << 31),
"`mod` must be less than (1u << 31) = 2147483648.");
unsigned val;
public:
static constexpr unsigned get_mod() {
return mod;
}
constexpr ModInt() : val(0) {}
template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {}
template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
constexpr ModInt(T x) : val((unsigned) (x % mod)) {}
static constexpr ModInt raw(unsigned x) {
ModInt<mod> ret;
ret.val = x;
return ret;
}
constexpr unsigned get_val() const {
return val;
}
constexpr ModInt operator+() const {
return *this;
}
constexpr ModInt operator-() const {
return ModInt<mod>(0u) - *this;
}
constexpr ModInt &operator+=(const ModInt &rhs) {
val += rhs.val;
if (val >= mod)
val -= mod;
return *this;
}
constexpr ModInt &operator-=(const ModInt &rhs) {
if (val < rhs.val)
val += mod;
val -= rhs.val;
return *this;
}
constexpr ModInt &operator*=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.val % mod;
return *this;
}
constexpr ModInt &operator/=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.inv().val % mod;
return *this;
}
friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) += rhs;
}
friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) -= rhs;
}
friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) *= rhs;
}
friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) /= rhs;
}
constexpr ModInt pow(unsigned long long x) const {
ModInt<mod> ret = ModInt<mod>::raw(1);
ModInt<mod> self = *this;
while (x != 0) {
if (x & 1)
ret *= self;
self *= self;
x >>= 1;
}
return ret;
}
constexpr ModInt inv() const {
static_assert(is_prime(mod), "`mod` must be a prime number.");
assert(val != 0);
return this->pow(mod - 2);
}
friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
long long val;
is >> val;
x.val = val % mod + (val < 0 ? mod : 0);
return is;
}
friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
os << x.val;
return os;
}
friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
return lhs.val == rhs.val;
}
friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
return lhs.val != rhs.val;
}
};
[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;
[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;
#line 2 "data_structure/segment_tree.hpp"
#line 6 "data_structure/segment_tree.hpp"
#line 2 "data_structure/operations.hpp"
#include <limits>
#line 5 "data_structure/operations.hpp"
template <typename T>
struct Add {
using Value = T;
static Value id() {
return T(0);
}
static Value op(const Value &lhs, const Value &rhs) {
return lhs + rhs;
}
static Value inv(const Value &x) {
return -x;
}
};
template <typename T>
struct Mul {
using Value = T;
static Value id() {
return Value(1);
}
static Value op(const Value &lhs, const Value &rhs) {
return lhs * rhs;
}
static Value inv(const Value &x) {
return Value(1) / x;
}
};
template <typename T>
struct Min {
using Value = T;
static Value id() {
return std::numeric_limits<T>::max();
}
static Value op(const Value &lhs, const Value &rhs) {
return std::min(lhs, rhs);
}
};
template <typename T>
struct Max {
using Value = T;
static Value id() {
return std::numeric_limits<Value>::min();
}
static Value op(const Value &lhs, const Value &rhs) {
return std::max(lhs, rhs);
}
};
template <typename T>
struct Xor {
using Value = T;
static Value id() {
return T(0);
}
static Value op(const Value &lhs, const Value &rhs) {
return lhs ^ rhs;
}
static Value inv(const Value &x) {
return x;
}
};
template <typename Monoid>
struct Reversible {
using Value = std::pair<typename Monoid::Value, typename Monoid::Value>;
static Value id() {
return Value(Monoid::id(), Monoid::id());
}
static Value op(const Value &v1, const Value &v2) {
return Value(
Monoid::op(v1.first, v2.first),
Monoid::op(v2.second, v1.second));
}
};
#line 8 "data_structure/segment_tree.hpp"
template <typename Monoid>
class SegmentTree {
public:
using Value = typename Monoid::Value;
private:
int old_length;
int length;
std::vector<Value> node;
static int ceil2(int n) {
int l = 1;
while (l < n) {
l <<= 1;
}
return l;
}
public:
SegmentTree(int n) :
old_length(n),
length(ceil2(old_length)),
node(length << 1, Monoid::id()) {
assert(n >= 0);
}
SegmentTree(const std::vector<Value> &v) :
old_length((int) v.size()),
length(ceil2(old_length)),
node(length << 1, Monoid::id()) {
for (int i = 0; i < old_length; ++i) {
node[i + length] = v[i];
}
for (int i = length - 1; i > 0; --i) {
node[i] = Monoid::op(node[i << 1], node[i << 1 | 1]);
}
}
template <typename F>
SegmentTree(int n, const F &f) :
old_length(n), length(ceil2(n)), node(length << 1, Monoid::id()) {
assert(n >= 0);
for (int i = 0; i < old_length; ++i) {
node[i + length] = f(i);
}
for (int i = length - 1; i > 0; --i) {
node[i] = Monoid::op(node[i << 1], node[i << 1 | 1]);
}
}
const Value &operator[](int idx) const {
assert(idx >= 0 && idx < old_length);
return node[idx + length];
}
void update(int idx, Value val) {
assert(idx >= 0 && idx < old_length);
idx += length;
node[idx] = std::move(val);
while (idx != 1) {
idx >>= 1;
node[idx] = Monoid::op(node[idx << 1], node[idx << 1 | 1]);
}
}
Value prod(int l, int r) const {
assert(l >= 0 && l <= r && r <= old_length);
Value prodl = Monoid::id();
Value prodr = Monoid::id();
l += length;
r += length;
while (l != r) {
if (l & 1) {
prodl = Monoid::op(prodl, node[l++]);
}
if (r & 1) {
prodr = Monoid::op(node[--r], prodr);
}
l >>= 1;
r >>= 1;
}
return Monoid::op(prodl, prodr);
}
Value all_prod() const {
return node[1];
}
};
#line 8 "data_structure/test/point_set_range_composite.test.cpp"
using Mint = ModInt<mod998244353>;
struct Linear {
Mint a, b;
Linear() : a(Mint(1)), b(Mint(0)) {}
Linear(Mint _a, Mint _b) : a(_a), b(_b) {}
Mint operator()(Mint x) {
return a * x + b;
}
};
// f \circ g
Linear composite(const Linear &f, const Linear &g) {
return Linear(f.a * g.a, f.a * g.b + f.b);
}
struct Ops {
using Value = Linear;
static Value id() {
return Linear();
}
static Value op(const Value &x, const Value &y) {
return composite(y, x);
}
};
int main() {
i32 n, q;
cin >> n >> q;
Vec<Linear> fs(n);
REP(i, n) {
cin >> fs[i].a >> fs[i].b;
}
SegmentTree<Ops> seg(fs);
REP(qi, q) {
i32 type;
cin >> type;
if (type == 0) {
i32 p;
Linear f;
cin >> p >> f.a >> f.b;
seg.update(p, f);
} else {
i32 l, r;
Mint x;
cin >> l >> r >> x;
cout << seg.prod(l, r)(x) << '\n';
}
}
}