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 ll long long
const int mod=1e9+7, nx=3e3+5;
ll h, w, dp[nx][nx], qs[nx][nx], ans[nx][nx];
int main()
{
cin.tie(NULL)->sync_with_stdio(false);
cin>>h>>w;
for (int i=1; i<=h; i++)
{
for (int j=1; j<=w; j++)
{
dp[i][j]=((ans[i-1][j-1]+1)*4)%mod;
dp[i][j]=(dp[i][j]+qs[i-1][j-1]*4*(j-1))%mod;
if (j>=2)
{
dp[i][j]=(dp[i][j]+(j-1)*(ans[i-1][j-2]+1))%mod;
dp[i][j]=(dp[i][j]+(j-1)*(j-2)/2*qs[i-1][j-2])%mod;
}
if (i>=2)
{
dp[i][j]=(dp[i][j]+(i-1)*(ans[i-2][j-1]+1))%mod;
dp[i][j]=(dp[i][j]+(j-1)*(i-1)*qs[i-2][j-1])%mod;
}
ans[i][j]=((ans[i-1][j]+ans[i][j-1]-ans[i-1][j-1]+dp[i][j])%mod+mod)%mod;
qs[i][j]=(qs[i-1][j]+dp[i][j])%mod;
}
}
cout<<ans[h][w];
}
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