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>
const int N = 2333,mo=1e9+7;
int n,k,f[N][N],g[N*N],fac[N];
int power(int a, int n){
	int res=1;
	while(n){
		if(n&1)res=1LL*res*a%mo;a=1LL*a*a%mo;n>>=1;
	}
	return res;
}
int main(){
	scanf("%d%d",&n,&k);if(k==1){puts("1");return 0;}
	for(int i=k-2,j=1;i<=n*k;i++)g[i]=j,j=1LL*j*(i+1)%mo*power(i-k+3,mo-2)%mo;
	fac[0]=1;for(int i=1;i<=n;i++)fac[i]=1LL*fac[i-1]*i%mo;
	for(int i=0;i<=n;i++)for(int j=i;j<=n;j++)
		if(i==0){
			if(j==0)f[i][j]=1;else f[i][j]=1LL*f[i][j-1]*g[i+j*k-j-1]%mo;
		}else f[i][j]=(f[i-1][j]+1LL*f[i][j-1]*g[i+j*k-j-1])%mo;
	printf("%lld",1LL*f[n][n]*fac[n]%mo);
	return 0;
}