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;
#define endl '\n'
#define pb(x) push_back(x)
#define mr(x, y) make_pair(x, y)
#define sz(x) (int)x.size()
#define S second
#define F first
const int N = 3e3 + 10;
const int MOD = 1e9 + 7;
long long dp[N][N], c[N][N], fact[N], pw[N];
int main(){
int h, w;
cin >> h >> w;
pw[0] = 1;
fact[0] = 1;
for(int i = 0; i < N; i++)
c[i][0] = 1;
for(int i = 1; i < N; i++){
fact[i] = fact[i - 1] * i;
fact[i] %= MOD;
pw[i] = pw[i - 1] * 4;
pw[i] %= MOD;
for(int j = 1; j <= i; j++){
c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % MOD;
}
}
for(int i = 0; i < N; i++){
dp[0][i] = 1;
dp[i][0] = 1;
}
for(int i = 1; i <= h; i++){
for(int j = 1; j <= w; j++){
dp[i][j] += dp[i - 1][j];
dp[i][j] %= MOD;
if(j >= 2)
dp[i][j] += c[j][2] * dp[i - 1][j - 2];
dp[i][j] %= MOD;
if(i >= 2)
dp[i][j] += j * (i - 1) * dp[i - 2][j - 1];
dp[i][j] %= MOD;
}
}
long long ans = 0;
for(int k = 1; k <= min(h, w); k++){
ans += ((((((c[h][k] * c[w][k]) % MOD) * fact[k]) % MOD) * dp[h - k][w - k]) % MOD) * pw[k];
ans %= MOD;
}
ans += dp[h][w];
ans %= MOD;
if(ans == 0)
cout << MOD - 1;
else
cout << ans - 1;
}
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