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 <iostream>
#include <cstdio>

#define MAX_N 2010
#define MX 4000010
#define MOD 1000000007

using std::cerr;
using std::endl;

int N, K, f[MAX_N][MAX_N];
int fac[MX], ifac[MX], inv[MX];

int C(int x, int y){
	return 1ll * fac[x] * ifac[y] % MOD* ifac[x-y] % MOD;
}

int main(){
	fac[0] = ifac[0] = inv[1] = 1;
	for(int i = 2; i < MX; i++) 
		inv[i] = 1ll * (MOD-MOD/i) * inv[MOD%i] % MOD;
	for(int i = 1; i < MX; i++){
		fac[i] = 1ll * fac[i-1] * i % MOD;
		ifac[i] = 1ll * ifac[i-1] * inv[i] % MOD;
	}
	scanf("%d%d", &N, &K);
	if(K == 1){
		puts("1"); return 0;
	}
	for(int i = 0; i <= N; i++) f[i][0] = 1;
	for(int i = 1; i <= N; i++)
		for(int j = 1; j <= i; j++)
			f[i][j] = (f[i-1][j] + 1ll * f[i][j-1] * C((N-j+1)*(K-1)+(N-i)-1, K-2) % MOD) % MOD;
	f[N][N] = 1ll * f[N][N] * fac[N] % MOD;
	printf("%d\n", f[N][N]);
	return 0;
}