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;
using ll = long long;
#define int long long
#define FOR(i, a, b) for (int i = (a); i <= (b); i++)
#define FORD(i, a, b) for (int i = (b); i >= (a); i --)
#define REP(i, a) for (int i = 0; i < (a); ++i)
#define REPD(i, a) for (int i = (a) - 1; i >= 0; --i)
#define MASK(i) (1LL << (i))
#define BIT(x, i) (((x) >> (i)) & 1)
constexpr ll LINF = (1ll << 60);
constexpr int INF = (1ll << 30);
constexpr int Mod = 1e9 + 7;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
/*
Phu Trong from Nguyen Tat Thanh High School for gifted student
*/
template <class X, class Y>
bool minimize(X &x, const Y &y){
X eps = 1e-9;
if (x > y + eps) {x = y; return 1;}
return 0;
}
template <class X, class Y>
bool maximize(X &x, const Y &y){
X eps = 1e-9;
if (x + eps < y) {x = y; return 1;}
return 0;
}
#define MAX 4444
int N, M;
int chooseTwo(int x){
return x * (x - 1) / 2 % Mod;
}
void add(int &x, int y){
x += y;
if (x >= Mod) x %= Mod;
}
int mul(int a, int b){
return 1LL * a * b % Mod;
}
int dp[MAX][MAX];
void process(void){
cin >> N >> M;
for (int i = 0; i <= N; ++i) dp[i][0] = 1;
for (int i = 0; i <= M; ++i) dp[0][i] = 1;
for (int i = 1; i <= N; ++i){
for (int j = 1; j <= M; ++j){
add(dp[i][j], dp[i - 1][j]);
if(j >= 2) add(dp[i][j], mul(dp[i - 1][j - 2], chooseTwo(j)));
if(i >= 2) add(dp[i][j], mul(mul(dp[i - 2][j - 1], i - 1), j));
add(dp[i][j], dp[i - 1][j - 1] * j * 4 % Mod);
}
}
cout << (dp[N][M] - 1 + Mod) % Mod;
}
signed main(){
#define name "Whisper"
cin.tie(nullptr) -> sync_with_stdio(false);
//freopen(name".inp", "r", stdin);
//freopen(name".out", "w", stdout);
process();
return (0 ^ 0);
}
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