This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
#define int long long
int dp[3003][3003];
int dv;
int bp(int a, int b){
if(b == 0) return 1;
if(b == 1) return a;
int k = bp(a, b/2);
k = (k * k) % mod;
if(b % 2 == 0) return k;
return (a * k) % mod;
}
int cal(int i, int j){
if(i < 0 || j < 0) return 0;
if(dp[i][j] != -1) return dp[i][j];
int ans = 0;
ans = (ans + cal(i - 1, j)) % mod;
ans = (ans + cal(i - 1, j - 2) * j % mod * (j - 1) % mod * dv % mod) % mod;
ans = (ans + cal(i - 2, j - 1) * j % mod * (i - 1) % mod) % mod;
ans = (ans + cal(i - 1, j - 1) * j % mod * 4 % mod) % mod;
return dp[i][j] = ans;
}
signed main(){
int n, m;
cin >> n >> m;
dv = bp(2, mod - 2);
for(int i = 0; i <= n; i++) for(int j = 0; j <= m; j++) dp[i][j] = -1;
for(int i = 0; i <= n; i++) dp[i][0] = 1;
for(int i = 0; i <= m; i++) dp[0][i] = 1;
cout << (cal(n, m) - 1 + mod)%mod;
return 0;
}
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