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>
#define L long long
using namespace std;
const int q=1000000007;
int n,m,a[4000010],b[4000010],f[2010][2010];
inline L C(int n,int m)
{
	return (L)a[n]*b[m]%q*b[n-m]%q;
}
int main()
{
	//freopen(".in","r",stdin);
	//fre,jopen(".out","w",stdout);
	int i,j;
	scanf("%d%d",&n,&m);
	if(m==1)
	  {
	   printf("1\n");
	   return 0;
	  }
	b[0]=b[1]=1;
	for(i=2;i<=n*m;i++)
	  b[i]=q-(L)q/i*b[q%i]%q;
	a[0]=1;
	for(i=1;i<=n*m;i++)
	  {
	   a[i]=(L)a[i-1]*i%q;
	   b[i]=(L)b[i-1]*b[i]%q;
	  }
	f[0][0]=1;
	for(i=0;i<=n;i++)
	  for(j=0;j<=i;j++)
	    {
		 if(i<n)
		   f[i+1][j]=(f[i+1][j]+f[i][j])%q;
		 if(j<i)
		   f[i][j+1]=(f[i][j+1]+f[i][j]*C(n*m-i-j*(m-1)-1,m-2))%q;
		}
	printf("%d\n",int((L)f[n][n]*a[n]%q));
	return 0;
}