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 <algorithm>
#define N 4006
#define mo 1000000007
using namespace std;
int n,k,f[N][N],fac[4000006],inv[4000006];
int ksm(int x,int y)
{
	if(y==0)return 1;if(y==1)return x;int p=ksm(x,y>>1);
	if(y&1)return 1LL*p*p%mo*x%mo;return 1LL*p*p%mo;
}
int C(int a,int b)
{
	return 1LL*fac[a]*inv[b]%mo*inv[a-b]%mo;
}
int main()
{
	scanf("%d%d",&n,&k);fac[0]=inv[0]=1;
	if(k==1)return puts("1"),0;
	for(int i=1;i<=n*k;i++)fac[i]=1LL*fac[i-1]*i%mo;
	inv[n*k]=ksm(fac[n*k],mo-2);
	for(int i=n*k-1;i>=1;i--)inv[i]=1LL*inv[i+1]*(i+1)%mo;
	f[1][1]=1;
	for(int i=2;i<=2*n;i++)
		for(int j=1;j<=min(i,n);j++){
			f[i][j]=f[i-1][j-1];
			if(j>=(i+1)/2)f[i][j]=(f[i][j]+1LL*f[i-1][j]*C(n*k-j-1-(k-1)*(i-j-1),k-2)%mo)%mo;
		}
	printf("%d\n",1LL*f[2*n][n]*fac[n]%mo);
}