結果
| 問題 | No.2499 Sum of Products of Sums |
| ユーザー |
 haruki_K
|
| 提出日時 | 2023-10-06 23:23:24 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 24,654 bytes |
| コンパイル時間 | 2,746 ms |
| コンパイル使用メモリ | 221,276 KB |
| 実行使用メモリ | 6,948 KB |
| 最終ジャッジ日時 | 2024-07-26 17:06:25 |
| 合計ジャッジ時間 | 17,779 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,816 KB |
| testcase_01 | AC | 2 ms
6,940 KB |
| testcase_02 | AC | 30 ms
6,940 KB |
| testcase_03 | AC | 2 ms
6,940 KB |
| testcase_04 | AC | 2 ms
6,944 KB |
| testcase_05 | AC | 2 ms
6,940 KB |
| testcase_06 | AC | 2 ms
6,940 KB |
| testcase_07 | AC | 18 ms
6,944 KB |
| testcase_08 | AC | 18 ms
6,940 KB |
| testcase_09 | AC | 17 ms
6,944 KB |
| testcase_10 | AC | 11 ms
6,940 KB |
| testcase_11 | AC | 27 ms
6,940 KB |
| testcase_12 | AC | 17 ms
6,940 KB |
| testcase_13 | AC | 1,508 ms
6,940 KB |
| testcase_14 | AC | 1,326 ms
6,948 KB |
| testcase_15 | AC | 849 ms
6,940 KB |
| testcase_16 | AC | 1,703 ms
6,944 KB |
| testcase_17 | TLE | - |
| testcase_18 | TLE | - |
| testcase_19 | TLE | - |
ソースコード
// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
#define int ll
using pii = pair<int, int>;
#define overload3(_1, _2, _3, f, ...) f
#define v1_rep(n) for (int _n = (n); _n--; )
#define v2_rep(i, n) if (const int _n = (n); true) for (int i = 0; i < _n; i++)
#define v3_rep(i, a, b) if (const int _b = (b); true) for (int i = (a); i < _b; i++)
#define rep(...) overload3(__VA_ARGS__, v3_rep, v2_rep, v1_rep)(__VA_ARGS__)
#define v2_repR(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define v3_repR(i, a, b) if (const int _a = (a); true) for (int i = int(b)-1; i >= _a; i--)
#define repR(...) overload3(__VA_ARGS__, v3_repR, v2_repR, v1_rep)(__VA_ARGS__)
#define rep1(i, n) if (const int _rep_n = n; true) for (int i = 1; i <= _rep_n; i++)
#define rep1R(i, n) for (int i = (int)(n); i >= 1; i--)
#define loop(i, a, B) for (int i = a; i B; i++)
#define loopR(i, a, B) for (int i = a; i B; i--)
#define all(x) begin(x), end(x)
#define allR(x) rbegin(x), rend(x)
#define pb push_back
#define eb emplace_back
#define fst first
#define snd second
template <class Int> auto constexpr inf_ = numeric_limits<Int>::max()/2-1;
auto constexpr INF32 = inf_<int32_t>;
auto constexpr INF64 = inf_<int64_t>;
auto constexpr INF = inf_<int>;
#ifdef LOCAL
#include "debug.hpp"
#define oj_local(x, y) (y)
#else
#define dump(...) ([]() { return false; }())
#define if_debug if (0)
#define oj_local(x, y) (x)
#endif
template <class T, class Comp> struct pque : priority_queue<T, vector<T>, Comp> {
vector<T> &data() { return this->c; }
void clear() { this->c.clear(); }
};
template <class T> using pque_max = pque<T, less<T>>;
template <class T> using pque_min = pque<T, greater<T>>;
template <class T, class S> ostream& operator<<(ostream& os, pair<T, S> const& p) {
return os << p.first << " " << p.second;
}
template <class T, class S> istream& operator>>(istream& is, pair<T, S>& p) {
return is >> p.first >> p.second;
}
template <class... T> ostream& operator<<(ostream& os, tuple<T...> const& t) {
bool f = true;
apply([&](auto&&... x) { ((os << (f ? f = false, "" : " ") << x), ...); }, t);
return os;
}
template <class... T> istream& operator>>(istream& is, tuple<T...>& t) {
apply([&](auto&&... x) { ((is >> x), ...); }, t);
return is;
}
template <class T, class = typename T::iterator, enable_if_t<!is_same<T, string>::value, int> = 0>
ostream& operator<<(ostream& os, T const& a) {
bool f = true;
for (auto const& x : a) os << (f ? "" : " ") << x, f = false;
return os;
}
template <class T, size_t N, enable_if_t<!is_same<T, char>::value, int> = 0>
ostream& operator<<(ostream& os, const T (&a)[N]) {
bool f = true;
for (auto const& x : a) os << (f ? "" : " ") << x, f = false;
return os;
}
template <class T, class = decltype(begin(declval<T&>())), class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; }
struct IOSetup {
IOSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
}
} iosetup;
template <class F> struct FixPoint : private F {
constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
template <class... T> constexpr auto operator()(T&&... x) const {
return F::operator()(*this, forward<T>(x)...);
}
};
struct MakeFixPoint {
template <class F> constexpr auto operator|(F&& f) const {
return FixPoint<F>(forward<F>(f));
}
};
#define def(name, ...) auto name = MakeFixPoint() | [&](auto &&name, __VA_ARGS__)
template <class F> struct FixPoint_d : private F {
const char* const name;
static inline int level = 0;
constexpr FixPoint_d(F&& f, const char* name) : F(forward<F>(f)), name(name) {}
template <class... T> constexpr auto operator()(T&&... x) const {
if constexpr (is_same_v<void, decltype(F::operator()(*this, forward<T>(x)...))>) {
#ifdef LOCAL
cerr << string(level, '|') << name << to_s(tuple(x...)) << '\n';
#endif
++level;
F::operator()(*this, forward<T>(x)...);
--level;
#ifdef LOCAL
cerr << string(level, '|') << name << to_s(tuple(x...)) << " -> void" << '\n';
#endif
} else {
#ifdef LOCAL
cerr << string(level, '|') << name << to_s(tuple(x...)) << '\n';
#endif
++level;
auto ret = F::operator()(*this, forward<T>(x)...);
--level;
#ifdef LOCAL
cerr << string(level, '|') << name << to_s(tuple(x...)) << " -> " << to_s(ret) << '\n';
#endif
return ret;
}
}
};
struct MakeFixPoint_d {
const char* const name;
MakeFixPoint_d(const char* name) : name(name) {}
template <class F> constexpr auto operator|(F&& f) const {
return FixPoint_d<F>(forward<F>(f), name);
}
};
#ifdef LOCAL
#define def_d(name, ...) auto name = MakeFixPoint_d(#name) | [&](auto &&name, __VA_ARGS__)
#else
#define def_d def
#endif
struct Reader {
template <class T> T get() const{ T x; cin >> x; return x; }
template <class T> operator T() const { return get<T>(); }
template <class... T> void operator()(T&... args) const { ((cin >> args), ...); }
} input;
namespace impl {
template <class T, size_t d> struct mvec { using type = vector<typename mvec<T, d-1>::type>; };
template <class T> struct mvec<T, 0> { using type = T; };
template <size_t i, size_t... j>
constexpr size_t head(index_sequence<i, j...>) { return i; }
template <size_t i, size_t... j>
constexpr auto tail(index_sequence<i, j...>) { return index_sequence<j...>{}; }
template <class T, size_t... i, size_t d, class Value>
auto make_v(index_sequence<i...>, const int (&s)[d], Value const& x) {
if constexpr (sizeof...(i) == 0) {
return (T)x;
} else {
typename mvec<T, sizeof...(i)>::type ret;
auto idx = index_sequence<i...>{};
int n = s[head(idx)];
if (n < 0) cerr << "[error] negative size: {" << s << "}\n", abort();
ret.reserve(n);
while (n-- > 0) ret.emplace_back(make_v<T>(tail(idx), s, x));
return ret;
}
}
} // namespace impl
template <class T, size_t d = 1> using mvec = typename impl::mvec<T, d>::type;
template <class T, size_t d, class Value> auto make_v(const int (&s)[d], Value const& x) {
return impl::make_v<T>(make_index_sequence<d>{}, s, x);
}
template <class T, size_t d> auto make_v(const int (&s)[d]) {
return impl::make_v<T>(make_index_sequence<d>{}, s, T{});
}
template <class T, class... Size> auto make_v(Size... s) {
return impl::make_v<T>(make_index_sequence<sizeof...(s)>{}, (int[sizeof...(s)]){s...}, T{});
}
template <class T> void quit(T const& x) { cout << x << '\n'; exit(0); }
template <class T, class U> constexpr bool chmin(T& x, U const& y) {
return x > y ? x = y, true : false;
}
template <class T, class U> constexpr bool chmax(T& x, U const& y) {
return x < y ? x = y, true : false;
}
template <class It> constexpr auto sumof(It b, It e) {
return accumulate(b, e, typename iterator_traits<It>::value_type{});
}
template <class T, class = decltype(begin(declval<T&>()))>
constexpr auto min(T const& a) { return *min_element(begin(a), end(a)); }
template <class T, class = decltype(begin(declval<T&>()))>
constexpr auto max(T const& a) { return *max_element(begin(a), end(a)); }
template <class T> constexpr T min(set<T> const& st) { assert(st.size()); return *st.begin(); }
template <class T> constexpr T max(set<T> const& st) { assert(st.size()); return *prev(st.end()); }
template <class T> constexpr T min(multiset<T> const& st) { assert(st.size()); return *st.begin(); }
template <class T> constexpr T max(multiset<T> const& st) { assert(st.size()); return *prev(st.end()); }
constexpr ll max(signed x, ll y) { return max<ll>(x, y); }
constexpr ll max(ll x, signed y) { return max<ll>(x, y); }
constexpr ll min(signed x, ll y) { return min<ll>(x, y); }
constexpr ll min(ll x, signed y) { return min<ll>(x, y); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T>
int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x) - begin(v); }
template <class C, class T>
int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x) - begin(v); }
constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; }
constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); }
constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); }
constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 };
constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 };
vector<int> iota(int n) {
vector<int> idx(n);
iota(begin(idx), end(idx), 0);
return idx;
}
template <class Comp> vector<int> iota(int n, Comp comp) {
vector<int> idx(n);
iota(begin(idx), end(idx), 0);
stable_sort(begin(idx), end(idx), comp);
return idx;
}
constexpr int popcnt(ll x) { return __builtin_popcountll(x); }
mt19937_64 seed_{random_device{}()};
template <class Int> Int rand(Int a, Int b) { return uniform_int_distribution<Int>(a, b)(seed_); }
i64 irand(i64 a, i64 b) { return rand<i64>(a, b); } // [a, b]
u64 urand(u64 a, u64 b) { return rand<u64>(a, b); } //
template <class It> void shuffle(It l, It r) { shuffle(l, r, seed_); }
template <class V> V &operator--(V &v) { for (auto &x : v) --x; return v; }
template <class V> V &operator++(V &v) { for (auto &x : v) ++x; return v; }
bool next_product(vector<int> &v, int m) {
repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0;
return false;
}
bool next_product(vector<int> &v, vector<int> const& s) {
repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0;
return false;
}
template <class Vec> int sort_unique(Vec &v) {
sort(begin(v), end(v));
v.erase(unique(begin(v), end(v)), end(v));
return v.size();
}
template <class Vec, class Comp> int sort_unique(Vec &v, Comp comp) {
sort(begin(v), end(v), comp);
v.erase(unique(begin(v), end(v)), end(v));
return v.size();
}
template <class It> auto prefix_sum(It l, It r) {
vector<typename It::value_type> s = { 0 };
while (l != r) s.emplace_back(s.back() + *l++);
return s;
}
template <class It> auto suffix_sum(It l, It r) {
vector<typename It::value_type> s = { 0 };
while (l != r) s.emplace_back(*--r + s.back());
reverse(s.begin(), s.end());
return s;
}
template <class T> T pop(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T> T pop_back(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T, class V, class C> T pop(priority_queue<T, V, C> &a) { auto x = a.top(); a.pop(); return x; }
template <class T> T pop(queue<T> &a) { auto x = a.front(); a.pop(); return x; }
template <class T> T pop_front(deque<T> &a) { auto x = a.front(); a.pop_front(); return x; }
template <class T> T pop_back(deque<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T> T pop_front(set<T> &a) { auto x = *a.begin(); a.erase(a.begin()); return x; }
template <class T> T pop_back(set<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
template <class T> T pop_front(multiset<T> &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; }
template <class T> T pop_back(multiset<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
template <class A, class B>
pair<vector<A>, vector<B>> unzip(vector<pair<A, B>> const& c) {
vector<A> a;
vector<B> b;
for (auto const& [x, y] : c) {
a.push_back(x);
b.push_back(y);
}
return { a, b };
}
template <class A, class B>
pair<vector<A>, vector<B>> unzip(map<A, B> const& c) {
vector<A> a;
vector<B> b;
for (auto const& [x, y] : c) {
a.push_back(x);
b.push_back(y);
}
return { a, b };
}
template <class T, class... Int> auto read_v(Int... s) {
auto x = make_v<T>(s...);
cin >> x;
return x;
}
template <class T> auto read_v() {
T x;
cin >> x;
return x;
}
template <class... T, class... Int>
auto read(Int... s) {
if constexpr (sizeof...(T) >= 2) {
return read_v<tuple<T...>>(s...);
} else {
return read_v<T...>(s...);
}
}
template <class T, size_t d, class... Int>
auto read(Int... s) {
return read_v<array<T, d>>(s...);
}
// <<<
constexpr int64_t MOD = 998244353;
// >>> modint, mod table
// >>> modint
template <uint32_t md> class modint {
static_assert(md < (1u<<31), "");
using M = modint;
using i64 = int64_t;
uint32_t x;
public:
static constexpr uint32_t mod = md;
constexpr modint(i64 x = 0) : x((x%=md) < 0 ? x+md : x) { }
constexpr i64 val() const { return x; }
constexpr explicit operator i64() const { return x; }
constexpr bool operator==(M r) const { return x == r.x; }
constexpr bool operator!=(M r) const { return x != r.x; }
constexpr M operator+() const { return *this; }
constexpr M operator-() const { return M()-*this; }
constexpr M& operator+=(M r) { x += r.x; x = (x < md ? x : x-md); return *this; }
constexpr M& operator-=(M r) { x += md-r.x; x = (x < md ? x : x-md); return *this; }
constexpr M& operator*=(M r) { x = (uint64_t(x)*r.x)%md; return *this; }
constexpr M& operator/=(M r) { return *this *= r.inv(); }
constexpr M operator+(M r) const { return M(*this) += r; }
constexpr M operator-(M r) const { return M(*this) -= r; }
constexpr M operator*(M r) const { return M(*this) *= r; }
constexpr M operator/(M r) const { return M(*this) /= r; }
friend constexpr M operator+(i64 x, M y) { return M(x)+y; }
friend constexpr M operator-(i64 x, M y) { return M(x)-y; }
friend constexpr M operator*(i64 x, M y) { return M(x)*y; }
friend constexpr M operator/(i64 x, M y) { return M(x)/y; }
constexpr M inv() const { assert(x > 0); return pow(md-2); }
constexpr M pow(i64 n) const {
// assert(not (x == 0 and n == 0));
if (n < 0) return inv().pow(-n);
M v = *this, r = 1;
for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v;
return r;
}
#ifdef LOCAL
friend string to_s(M r) { return to_s(r.val(), mod); }
#endif
friend ostream& operator<<(ostream& os, M r) { return os << r.val(); }
friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; }
};
// <<<
using mint = modint<MOD>;
mint sign(int n) { return n & 1 ? -1 : +1; }
// >>> mod table
template <uint32_t mod> struct ModTable {
static_assert(mod > 1, "");
vector<uint32_t> fact = { 1, 1 }, finv = { 1, 1 }, inv = { 0, 1 };
ModTable(int n = 0) {
calc(n);
}
void calc(int n) {
const int now = fact.size();
if (n < now) return;
assert(n < int(1e9));
int nxt = now;
do nxt <<= 1; while (nxt <= n);
fact.resize(nxt);
finv.resize(nxt);
inv.resize(nxt);
for (uint32_t i = now; i < nxt; i++) {
fact[i] = uint64_t(fact[i-1]) * i % mod;
inv[i] = mod - uint64_t(inv[mod%i]) * (mod/i) % mod;
finv[i] = uint64_t(finv[i-1]) * inv[i] % mod;
}
}
};
ModTable<MOD> mod_tab;
modint<MOD> fact(int n) {
assert(0 <= n);
mod_tab.calc(n);
return mod_tab.fact[n];
}
modint<MOD> finv(int n) {
assert(0 <= n);
mod_tab.calc(n);
return mod_tab.finv[n];
}
modint<MOD> inv(int n) {
assert(0 <= n);
mod_tab.calc(n);
return mod_tab.inv[n];
}
modint<MOD> comb(int n, int k) {
if (k < 0) {
return 0;
} else if (n >= k) {
mod_tab.calc(n);
return (uint64_t)mod_tab.finv[k] * mod_tab.finv[n-k] % MOD * mod_tab.fact[n];
} else if (n < 0) {
n = -n+k-1;
mod_tab.calc(n);
int ans = (uint64_t)mod_tab.finv[k] * mod_tab.finv[n-k] % MOD * mod_tab.fact[n];
if (k & 1) ans = -ans;
return ans;
} else {
return 0;
}
}
// <<<
// <<<
// >>> NTT
template <class ModInt, int64_t g>
struct NTT {
using modint = ModInt;
static constexpr int64_t mod = ModInt::mod, gen = g, max_lg = __builtin_ctzll(mod-1);
// mod:prime, g:primitive root
static_assert(mod > 0 && g > 0 && max_lg > 0, "");
using arr_t = array<ModInt, max_lg+1>;
static inline const arr_t ws = []() {
arr_t ret;
for (int i = 0; i <= max_lg; i++) {
ret[i] = -ModInt(g).pow((mod-1)>>(i+2));
}
return ret;
} ();
static inline const arr_t iws = []() {
arr_t ret;
for (int i = 0; i <= max_lg; i++) {
ret[i] = -ModInt(1)/ModInt(g).pow((mod-1)>>(i+2));
}
return ret;
} ();
static void ntt(ModInt a[], int lg) {
for (int b = lg-1; b >= 0; b--) {
ModInt w = 1;
for (int i = 0, k = 0; i < (1<<lg); i += 1<<(b+1)) {
for (int j = i; j < (i|(1<<b)); j++) {
const int k = j|(1<<b);
const auto x = a[j], y = a[k];
a[j] = x + y*w;
a[k] = x - y*w;
}
w *= ws[__builtin_ctz(++k)];
}
}
// bit_reverse(a, 1<<lg);
}
static void intt(ModInt a[], int lg) {
// bit_reverse(a, 1<<lg);
for (int b = 0; b < lg; b++) {
ModInt w = 1;
for (int i = 0, k = 0; i < (1<<lg); i += 1<<(b+1)) {
for (int j = i; j < (i|(1<<b)); j++) {
const int k = j|(1<<b);
const auto x = a[j], y = a[k];
a[j] = x + y;
a[k] = w*(x - y);
}
w *= iws[__builtin_ctz(++k)];
}
}
}
template <class T>
static vector<ModInt> conv(vector<T> const& a, vector<T> const& b) {
if (a.empty() || b.empty()) return {};
const int s = a.size() + b.size() - 1, lg = __lg(2*s-1);
assert(lg <= max_lg);
vector<ModInt> aa(1<<lg);
rep (i, a.size()) aa[i] = (int64_t)a[i];
ntt(aa.data(), lg);
vector<ModInt> bb(1<<lg);
rep (i, b.size()) bb[i] = (int64_t)b[i];
ntt(bb.data(), lg);
const auto x = ModInt(1)/ModInt(1<<lg);
rep (i, 1<<lg) aa[i] *= bb[i]*x;
intt(aa.data(), lg); aa.resize(s);
return aa;
}
template <class T>
static vector<ModInt> conv(vector<T> const& a) {
if (a.empty()) return {};
const int s = a.size()*2 - 1, lg = __lg(2*s-1);
assert(lg <= max_lg);
vector<ModInt> aa(1<<lg);
rep (i, a.size()) aa[i] = (int64_t)a[i];
ntt(aa.data(), lg);
const auto x = ModInt(1)/ModInt(1<<lg);
rep (i, 1<<lg) aa[i] *= aa[i]*x;
intt(aa.data(), lg); aa.resize(s);
return aa;
}
};
// <<<
using ntt = NTT<mint, 3>;
// >>> FPS
template <class NTT>
struct FormalPowerSeries : NTT, vector<typename NTT::modint> {
using mint = typename NTT::modint;
using NTT::conv;
using vector<mint>::vector; // inherit constructors
using FPS = FormalPowerSeries;
FormalPowerSeries() : vector<mint>() {}
FormalPowerSeries(vector<mint> const& v) : vector<mint>(v) {}
FormalPowerSeries(mint const& x) : vector<mint>({x}) {}
void shrink() { while (this->size() and this->back() == 0) this->pop_back(); }
mint get(int i) const {
assert(i >= 0);
if (i < (int)this->size()) return (*this)[i];
else return 0;
}
mint &set(int i, mint x) {
assert(i >= 0);
if (i >= (int)this->size()) this->resize(i+1);
return (*this)[i] = x;
}
bool operator==(FPS const& r) const {
const int n = min(this->size(), r.size());
rep (i, n) {
if ((*this)[i] != r[i]) return false;
}
for (int i = n; i < (int)this->size(); ++i) {
if ((*this)[i] != mint(0)) return false;
}
for (int i = n; i < (int)r.size(); ++i) {
if (r[i] != mint(0)) return false;
}
return true;
}
bool operator!=(FPS const& r) const { return !((*this) == r); }
FPS operator+(FPS const& r) const { return FPS(*this) += r; }
FPS operator-(FPS const& r) const { return FPS(*this) -= r; }
FPS& operator+=(FPS const& r) {
if (r.size() > this->size()) this->resize(r.size());
rep (i, r.size()) (*this)[i] += r[i];
return *this;
}
FPS& operator-=(FPS const& r) {
if (r.size() > this->size()) this->resize(r.size());
rep (i, r.size()) (*this)[i] -= r[i];
return *this;
}
FPS operator*(FPS const& r) const {
if (this->empty() || r.empty()) return {};
return conv(*this, r);
}
FPS& operator*=(FPS const& r) { return *this = *this * r; }
friend FPS operator+(mint const& x, FPS const& f) { return FPS{x}+f; }
friend FPS operator-(mint const& x, FPS const& f) { return FPS{x}-f; }
friend FPS operator*(mint const& x, FPS const& f) { return FPS{x}*f; }
friend FPS operator+(FPS const& f, mint const& x) { return f+FPS{x}; }
friend FPS operator-(FPS const& f, mint const& x) { return f-FPS{x}; }
friend FPS operator*(FPS const& f, mint const& x) { return f*FPS{x}; }
friend FPS operator+(FPS const& f) { return f; }
friend FPS operator-(FPS const& f) { return FPS{}-f; }
FPS take(int sz) const {
FPS ret(this->begin(), this->begin() + min<int>(this->size(), sz));
ret.resize(sz);
return ret;
}
FPS inv(int sz = -1) const {
assert(this->size()); assert((*this)[0] != mint(0));
if (sz < 0) sz = this->size();
FPS ret = { mint(1)/(*this)[0] };
for (int i = 1; i < sz; i <<= 1) {
ret = ret + ret - ret*ret*take(i<<1);
ret.resize(i<<1);
}
ret.resize(sz);
return ret;
}
FPS diff() const {
FPS ret(max<int>(0, this->size()-1));
rep (i, ret.size()) ret[i] = (*this)[i+1]*mint(i+1);
return ret;
}
FPS integral() const {
FPS ret(this->size()+1);
ret[0] = 0;
rep (i, this->size()) ret[i+1] = (*this)[i]/mint(i+1);
return ret;
}
FPS log(int sz = -1) const {
assert(this->size()); assert((*this)[0] == mint(1));
if (sz < 0) sz = this->size();
return (diff()*inv(sz)).take(sz-1).integral();
}
// FPS log(int sz = -1) const {
// assert(this->size()); assert((*this)[0] == mint(1));
// if (sz < 0) sz = this->size();
// auto ret = diff()*inv(sz);
// ret.resize(sz);
// for (int i = sz-1; i > 0; --i) ret[i] = ret[i-1]/mint(i);
// ret[0] = 0;
// return ret;
// }
FPS exp(int sz = -1) const {
FPS ret = {mint(1)};
if (this->empty()) return ret;
assert((*this)[0] == mint(0));
if (sz < 0) sz = this->size();
for (int i = 1; i < sz; i <<= 1) {
ret *= take(i<<1) + mint(1) - ret.log(i<<1);
ret.resize(i<<1);
}
ret.resize(sz);
return ret;
}
FPS pow(int64_t k, int sz = -1) const {
if (sz < 0) sz = this->size();
int deg = 0;
while (deg < sz && (*this).get(deg) == mint(0)) ++deg;
assert(k >= 0 || deg == 0);
auto c = mint(1)/(*this).get(deg);
FPS ret(sz-deg);
rep (i, sz-deg) ret[i] = (*this).get(deg+i)*c;
ret = (ret.log()*k).exp() * (*this).get(deg).pow(k);
ret.resize(sz);
for (int i = sz-1; i >= 0; --i) {
int j = i-deg*k;
ret[i] = (j >= 0 ? ret[j] : mint(0));
}
return ret;
}
mint eval(mint x) const {
mint p = 1, ret = 0;
rep (i, this->size()) {
ret += (*this)[i] * p;
p *= x;
}
return ret;
}
};
// <<<
using FPS = FormalPowerSeries<ntt>;
int32_t main() {
int n = input, m = input;
FPS dp = {1};
rep (n) {
int a = input, b = input;
--a;
cerr << a << " " << b << endl;
FPS f(m + 1);
mint B = finv(m), A = finv(m);
rep (j, m) B *= m + b - j, A *= m + a - j;
rep (k, f.size()) {
if (k > 0) {
mint c = mint(m + k).inv();
B *= (b - k + 1) * c;
A *= (a - k + 1) * c;
}
f[k] = (B - A) * finv(k);
}
cerr << f << endl;
dump(f);
dp *= f;
dp.resize(m + 1);
}
cout << dp[m] * fact(m) << '\n';
}