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<bits/stdc++.h>
typedef long long i64;
const int P=1e9+7,N=2007;
int pw(int a,int n){
	int v=1;
	for(;n;n>>=1,a=(i64)a*a%P)if(n&1)v=(i64)v*a%P;
	return v;
}
int fac[N*N],fiv[N*N],mx;
int n,k,f[N];
int C(int n,int m){
	return (i64)fac[n]*fiv[m]%P*fiv[n-m]%P;
}
int main(){
	scanf("%d%d",&n,&k);
	if(k==1)return puts("1"),0;
	mx=n*k;
	for(int i=fac[0]=1;i<=mx;++i)fac[i]=i64(i)*fac[i-1]%P;
	fiv[mx]=pw(fac[mx],P-2);
	for(int i=mx;i;--i)fiv[i-1]=i64(i)*fiv[i]%P;
	f[1]=1;
	for(int i=1;i<=n;++i){
		for(int j=1,s=0;j<=i;++j){
			s=(s+f[j])%P;
			f[j]=(i64)s*C(i*(k-1)+j-2,k-2)%P;
		}
	}
	int ans=0;
	for(int i=1;i<=n;++i)ans=(ans+f[i])%P;
	ans=(i64)ans*fac[n]%P;
	printf("%d\n",ans);
	return 0;
}