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:
// luogu-judger-enable-o2
#include<bits/stdc++.h>
using namespace std;
const int M=1e9+7,N=2002*2002;
int pw(int x,int y){
	int z=1;
	for (;y;y>>=1,x=1ll*x*x%M)
		if (y&1) z=1ll*z*x%M;
	return z;
}
int INV(int x){return pw(x,M-2);}
int fac[N],inv[N],f[2002][2002],i,j,n,k;
int C(int n,int m){return 1ll*fac[n]*inv[m]%M*inv[n-m]%M;}
int main(){
	scanf("%d%d",&n,&k);
	if (k==1) return puts("1"),0;
	fac[0]=1;
	for (i=1;i<N;i++) fac[i]=1ll*fac[i-1]*i%M;
	inv[N-1]=INV(fac[N-1]);
	for (i=N-2;~i;i--) inv[i]=1ll*inv[i+1]*(i+1)%M;
	for (i=0;i<=n;i++)
		for (f[i][0]=1,j=1;j<=i;j++) f[i][j]=(f[i-1][j]+1ll*f[i][j-1]*(n-j+1)%M*C(n*k-i-(j-1)*(k-1)-1,k-2)%M)%M;
	printf("%d",f[n][n]);
}