// >>> 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'; }