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 <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#define LL long long
using namespace std;
const LL Maxn = 2010;
const LL Mod = 1e9+7;
LL n, m;
LL f[Maxn][Maxn];
LL jc[Maxn*Maxn], inv[Maxn*Maxn];
LL C(LL A, LL B) { return jc[A]*inv[B]%Mod*inv[A-B]%Mod; }
void up(LL &x, LL y) { x = (x+y)%Mod; }
int main() {
	LL i, j, k;
	scanf("%lld%lld", &n, &m);
	if(m == 1){ printf("1\n"); return 0; }
	jc[0] = 1;
	for(i = 1; i <= n*m; i++) jc[i] = jc[i-1]*i%Mod;
	inv[0] = inv[1] = 1;
	for(i = 2; i <= n*m; i++) inv[i] = inv[Mod%i]*(Mod-Mod/i)%Mod;
	for(i = 2; i <= n*m; i++) inv[i] = inv[i]*inv[i-1]%Mod;
	f[0][0] = 1;
	for(i = 0; i <= n; i++){
		for(j = i; j <= n; j++){
			if(i < j) up(f[i+1][j], f[i][j]);
			if(j < n) up(f[i][j+1], C((m-1)*(j+1)+i-1,m-2)*f[i][j]);
		}
	}
	printf("%lld\n", f[n][n]*jc[n]%Mod);
	return 0;
}