#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...$){((cerr<<$<<"; "),...)<<'\n';}(x)
#else
#define debug(...) {}
#endif
int main() {
cin.tie(0)->sync_with_stdio(0);
constexpr LL mod = 1'000'000'007;
auto mno = [&](LL a, LL b) {
return a * b % mod;
};
auto pot = [&](LL a, LL b) {
LL z = 1;
while (b) {
if (b % 2) {
z = mno(z, a);
}
a = mno(a, a);
b /= 2;
}
return z;
};
int n, m;
cin >> n >> m;
const LL odwm = pot(m, mod - 2);
debug(n, m);
vector<vector<LL>> dp(n + 1, vector<LL>(n + 2));
vector<vector<LL>> dp2(n + 1, vector<LL>(n + 2));
dp[1][1] = m;
const int ogr = min(n, m);
FOR(i, 1, n - 1) {
FOR(j, 0, ogr) {
dp2[i + 1][j] += (dp2[i][j] + dp[i][j]) * j;
dp2[i + 1][j] %= mod;
dp[i + 1][j] += dp[i][j] * (m - j);
dp[i + 1][j] %= mod;
dp[i + 1][j + 1] += dp2[i][j] * (m - j);
dp[i + 1][j + 1] %= mod;
}
}
debug(dp);
debug(dp2);
LL ans = 0;
FOR(i, 0, n) {
ans += dp2[n][i];
}
ans %= mod;
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 | #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...$){((cerr<<$<<"; "),...)<<'\n';}(x) #else #define debug(...) {} #endif int main() { cin.tie(0)->sync_with_stdio(0); constexpr LL mod = 1'000'000'007; auto mno = [&](LL a, LL b) { return a * b % mod; }; auto pot = [&](LL a, LL b) { LL z = 1; while (b) { if (b % 2) { z = mno(z, a); } a = mno(a, a); b /= 2; } return z; }; int n, m; cin >> n >> m; const LL odwm = pot(m, mod - 2); debug(n, m); vector<vector<LL>> dp(n + 1, vector<LL>(n + 2)); vector<vector<LL>> dp2(n + 1, vector<LL>(n + 2)); dp[1][1] = m; const int ogr = min(n, m); FOR(i, 1, n - 1) { FOR(j, 0, ogr) { dp2[i + 1][j] += (dp2[i][j] + dp[i][j]) * j; dp2[i + 1][j] %= mod; dp[i + 1][j] += dp[i][j] * (m - j); dp[i + 1][j] %= mod; dp[i + 1][j + 1] += dp2[i][j] * (m - j); dp[i + 1][j + 1] %= mod; } } debug(dp); debug(dp2); LL ans = 0; FOR(i, 0, n) { ans += dp2[n][i]; } ans %= mod; cout << ans << '\n'; } |
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