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>
#define N 2010
#define mod 1000000007
int n,k,f[N*N],inv[N*N],a[N][N];
inline int C(int x,int y){
	return 1ll*f[x]*inv[y]%mod*inv[x-y]%mod;
}
int main(){
//	freopen("a.in","r",stdin);
	scanf("%d%d",&n,&k);if(k==1){puts("1");return 0;}
	f[0]=f[1]=1;for(int i=2;i<=n*k;++i) f[i]=1ll*f[i-1]*i%mod;
	inv[0]=inv[1]=1;for(int i=2;i<=n*k;++i) inv[i]=1ll*(mod-mod/i)*inv[mod%i]%mod;
	for(int i=2;i<=n*k;++i) inv[i]=1ll*inv[i-1]*inv[i]%mod;
	a[0][0]=1;
	for(int i=1;i<=n;++i){
		for(int j=0;j<=i;++j){
			a[i][j]=a[i-1][j];
			if(j) a[i][j]=(a[i][j]+1ll*(n-j+1)*C(n-i+(n-j+1)*(k-1)-1,k-2)%mod*a[i][j-1]%mod)%mod;
		}
	}
	printf("%d\n",a[n][n]);
	return 0;
}