This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ld, ld> pdd;
#define fi first
#define se second
#define mp make_pair
#define fastIO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
const int N = 3005;
const int MOD = (int)1e9 + 7;
int mult(int a, int b){
return (a * 1ll * b) % MOD;
}
void add(int &a, int b){
a = (a + b) % MOD;
}
int dp[N][N];
int solve(int i, int j){
if(dp[i][j] != -1) return dp[i][j];
dp[i][j] = 0;
if(i == 0 || j == 0){
dp[i][j] = 1;
}
else{
add(dp[i][j], solve(i - 1, j));
add(dp[i][j], mult(4 * j, solve(i - 1, j - 1)));
if(j > 1) add(dp[i][j], mult(j * (j - 1) / 2, solve(i - 1, j - 2)));
if(i > 1) add(dp[i][j], mult(mult(j, (i - 1)), solve(i - 2, j - 1)));
}
return dp[i][j];
}
int main(){
fastIO;
int n, m;
cin >> n >> m;
for(int i = 0 ; i <= n; i ++ ){
for(int j = 0 ; j <= m ; j ++ ){
dp[i][j] = -1;
}
}
cout << (solve(n, m) - 1 + MOD) % MOD;
return 0;
}
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