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;
#pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
// Ofast, O0, O1, O2, O3, unroll-loops, fast-math, trapv
typedef long long ll;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
#define Mp make_pair
#define sep ' '
#define endl '\n'
#define F first
#define S second
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define kill(res) cout << res << '\n', exit(0);
#define set_dec(x) cout << fixed << setprecision(x);
#define fast_io ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define file_io freopen("input.txt", "r", stdin) ; freopen("output.txt", "w", stdout);
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const ll N = 3e3 + 50;
const ll Mod = 1e9 + 7;
ll n, m, dp[N][N], inv2;
ll power(ll a, ll b, ll md = Mod){
ll ans = 1;
for(; b; b /= 2, a = a * a % md){
if(b % 2) ans = ans * a % md;
}
return ans;
}
ll c2(ll x){
return x * (x-1) % Mod * inv2 % Mod;
}
int main(){
fast_io;
inv2 = power(2, Mod-2);
cin >> n >> m;
dp[0][0] = 1;
for(int i = 1; i <= n; i++) dp[i][0] = 1;
for(int j = 1; j <= m; j++) dp[0][j] = 1;
for(int i = 1; i <= n; i++){
for(int j = 1; j <= m; j++){
dp[i][j] = (dp[i-1][j] + 4 * dp[i-1][j-1] * j) % Mod;
if(i > 1) dp[i][j] = (dp[i][j] + dp[i-2][j-1] * j * (i-1)) % Mod;
if(j > 1) dp[i][j] = (dp[i][j] + dp[i-1][j-2] * c2(j)) % Mod;
}
}
cout << (dp[n][m] - 1 + Mod) % Mod;
}
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