#include <bits/stdc++.h> using namespace std; using LL = long long; #define FOR(i, l, r) for(int i = (l); i <= (r); ++i) #define REP(i, n) FOR(i, 0, (n) - 1) #define ssize(x) int(x.size()) template<class A, class B> auto& operator<<(ostream &o, pair<A, B> p) { return o << '(' << p.first << ", " << p.second << ')'; } template<class T> auto operator<<(ostream &o, T x) -> decltype(x.end(), o) { o << '{'; int i = 0; for(auto e : x) o << (", ")+2*!i++ << e; return o << '}'; } #ifdef DEBUG #define debug(x...) cerr << "[" #x "]: ", [](auto... $) {((cerr << $ << "; "), ...); }(x), cerr << '\n' #else #define debug(...) {} #endif template<int mod> struct modular { int val; modular() { val = 0; } modular(const LL& v) { val = int((-mod <= v && v <= mod) ? (int) v : v % mod); if(val < 0) val += mod; } int to_int() { return val; } friend ostream& operator<<(ostream &os, const modular &a) { return os << a.val; } friend istream& operator>>(istream &is, modular &a) { return is >> a.val; } friend bool operator==(const modular &a, const modular &b) { return a.val == b.val; } friend bool operator!=(const modular &a, const modular &b) { return !(a == b); } friend bool operator<(const modular &a, const modular &b) { return a.val < b.val; } friend bool operator<=(const modular &a, const modular &b) { return a.val <= b.val; } modular operator-() const { return modular(-val); } modular& operator+=(const modular &m) { if((val += m.val) >= mod) val -= mod; return *this; } modular& operator-=(const modular &m) { if((val -= m.val) < 0) val += mod; return *this; } modular& operator*=(const modular &m) { val = (LL) val * m.val % mod; return *this; } friend modular qpow(modular a, LL n) { if(n == 0) return 1; if(n % 2 == 1) return qpow(a, n - 1) * a; return qpow(a * a, n / 2); } friend modular inv(const modular &a) { assert(a != 0); return qpow(a, mod - 2); } modular& operator/=(const modular &m) { return (*this) *= inv(m); } modular operator++(int) { modular res = (*this); (*this) += 1; return res; } friend modular operator+(modular a, const modular &b) { return a += b; } friend modular operator-(modular a, const modular &b) { return a -= b; } friend modular operator*(modular a, const modular &b) { return a *= b; } friend modular operator/(modular a, const modular &b) { return a /= b; } }; using mint = modular<int(1e9 + 7)>; // using mint = modular<998244353>; int main() { cin.tie(0)->sync_with_stdio(0); int n, m; cin >> n >> m; vector dp(n + 1, vector(n + 1, array<mint, 2>{0, 0})); dp[0][0][1] = 1; REP(i, n) { FOR(j, 1, n) { dp[i + 1][j][0] = dp[i][j - 1][1] * (m - j + 1) + dp[i][j][0] * (m - j); dp[i + 1][j][1] = (dp[i][j][0] + dp[i][j][1]) * j; } } mint ans = 0; FOR(j, 1, n) ans += dp[n][j][1]; cout << ans << "\n"; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 | #include <bits/stdc++.h> using namespace std; using LL = long long; #define FOR(i, l, r) for(int i = (l); i <= (r); ++i) #define REP(i, n) FOR(i, 0, (n) - 1) #define ssize(x) int(x.size()) template<class A, class B> auto& operator<<(ostream &o, pair<A, B> p) { return o << '(' << p.first << ", " << p.second << ')'; } template<class T> auto operator<<(ostream &o, T x) -> decltype(x.end(), o) { o << '{'; int i = 0; for(auto e : x) o << (", ")+2*!i++ << e; return o << '}'; } #ifdef DEBUG #define debug(x...) cerr << "[" #x "]: ", [](auto... $) {((cerr << $ << "; "), ...); }(x), cerr << '\n' #else #define debug(...) {} #endif template<int mod> struct modular { int val; modular() { val = 0; } modular(const LL& v) { val = int((-mod <= v && v <= mod) ? (int) v : v % mod); if(val < 0) val += mod; } int to_int() { return val; } friend ostream& operator<<(ostream &os, const modular &a) { return os << a.val; } friend istream& operator>>(istream &is, modular &a) { return is >> a.val; } friend bool operator==(const modular &a, const modular &b) { return a.val == b.val; } friend bool operator!=(const modular &a, const modular &b) { return !(a == b); } friend bool operator<(const modular &a, const modular &b) { return a.val < b.val; } friend bool operator<=(const modular &a, const modular &b) { return a.val <= b.val; } modular operator-() const { return modular(-val); } modular& operator+=(const modular &m) { if((val += m.val) >= mod) val -= mod; return *this; } modular& operator-=(const modular &m) { if((val -= m.val) < 0) val += mod; return *this; } modular& operator*=(const modular &m) { val = (LL) val * m.val % mod; return *this; } friend modular qpow(modular a, LL n) { if(n == 0) return 1; if(n % 2 == 1) return qpow(a, n - 1) * a; return qpow(a * a, n / 2); } friend modular inv(const modular &a) { assert(a != 0); return qpow(a, mod - 2); } modular& operator/=(const modular &m) { return (*this) *= inv(m); } modular operator++(int) { modular res = (*this); (*this) += 1; return res; } friend modular operator+(modular a, const modular &b) { return a += b; } friend modular operator-(modular a, const modular &b) { return a -= b; } friend modular operator*(modular a, const modular &b) { return a *= b; } friend modular operator/(modular a, const modular &b) { return a /= b; } }; using mint = modular<int(1e9 + 7)>; // using mint = modular<998244353>; int main() { cin.tie(0)->sync_with_stdio(0); int n, m; cin >> n >> m; vector dp(n + 1, vector(n + 1, array<mint, 2>{0, 0})); dp[0][0][1] = 1; REP(i, n) { FOR(j, 1, n) { dp[i + 1][j][0] = dp[i][j - 1][1] * (m - j + 1) + dp[i][j][0] * (m - j); dp[i + 1][j][1] = (dp[i][j][0] + dp[i][j][1]) * j; } } mint ans = 0; FOR(j, 1, n) ans += dp[n][j][1]; cout << ans << "\n"; } |