This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
/**
_ _ __ _ _ _ _ _ _
|a ||t ||o d | |o |
| __ _| | _ | __| _ |
| __ |/_ | __ /__\ / _\|
**/
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N_MAX = 3000;
const int MOD = (int) 1e9 + 7;
void add (int &x, const int &y) {
x += y;
if (x >= MOD) {
x -= MOD;
}
}
int N, M;
int dp[N_MAX + 2][N_MAX + 2];
int main () {
ios_base::sync_with_stdio(false);
cin.tie(0);
cin >> N >> M;
for (int n = 0; n <= N; n++) {
dp[n][0] = 1;
}
for (int m = 0; m <= M; m++) {
dp[0][m] = 1;
}
for (int n = 1; n <= N; n++) {
for (int m = 1; m <= M; m++) {
dp[n][m] = dp[n - 1][m];
add(dp[n][m], (ll) dp[n - 1][m - 1] * m * 4 % MOD);
if (m >= 2) {
add(dp[n][m], dp[n - 1][m - 2] * ((ll) m * (m - 1) / 2 % MOD) % MOD);
}
if (n >= 2) {
add(dp[n][m], (ll) dp[n - 2][m - 1] * m % MOD * (n - 1) % MOD);
}
}
}
cout << (dp[N][M] - 1 + MOD) % MOD << "\n";
return 0;
}
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