Problem: Snuke loves colorful balls. He has a total of N×K balls, K in each of his favorite N colors. The colors are numbered 1 through N.

He will arrange all of the balls in a row from left to right, in arbitrary order. Then, for each of the N colors, he will paint the leftmost ball of that color into color 0, a color different from any of the N original colors.

After painting, how many sequences of the colors of the balls are possible? Find this number modulo 10^9+7.

Constraints

* 1≤N,K≤2,000

Input

The input is given from Standard Input in the following format:


N K


Output

Print the number of the possible sequences of the colors of the balls after painting, modulo 10^9+7.

Examples

Input

2 2


Output

4


Input

3 1


Output

1


Input

2 3


Output

14


Input

2000 2000


Output

546381702

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

const int N = 2e3L + 11;
using ll = long long;
const ll mod = 1e9L + 7;

const int M = 1e7L + 11;
ll fac[M], inv[M];
ll binom(int n, int m) {
	return fac[n] * inv[m] % mod * inv[n - m] % mod;
}

ll f[N][N];

int main() {
	fac[0] = inv[0] = fac[1] = inv[1] = 1;
	for(int i = 2; i < M; i ++)
		inv[i] = (mod - mod / i) * inv[mod % i] % mod;
	for(int i = 2; i < M; i ++) {
		fac[i] = fac[i - 1] * i % mod;
		inv[i] = inv[i - 1] * inv[i] % mod;
	}
	ios :: sync_with_stdio(0);
	int n, m; cin >> n >> m;
	if(m == 1) {
		cout << "1\n";
		return 0;
	}
	f[0][0] = 1;
	for(int i = 0; i <= n; i ++)
		for(int j = 0; j <= n; j ++) {
			if(i) f[i][j] += f[i - 1][j];
			if(j) f[i][j] += f[i][j - 1] * binom(i + j * (m - 1) - 1, m - 2) % mod;
			f[i][j] %= mod;
			if(i > j) f[i][j] = 0;
		}

	ll ans = f[n][n] * fac[n] % mod;
	cout << ans << '\n';
}