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<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<iostream>
#define mmod 1000000007
#define N 2100
using namespace std;
int n,m,jc[N*N],ny[N*N],f[N][N],ans;
int C(int n,int m)
{
	return 1ll*jc[n]*ny[m]%mmod*ny[n-m]%mmod;
}
void upd(int &x,int y)
{
	x=(x+y)%mmod;
}
int main()
{
	scanf("%d%d",&n,&m);
	if(m==1) {printf("1\n");return 0;}
	jc[0]=jc[1]=ny[0]=ny[1]=1;
	for(int i=2;i<=n*m;i++) jc[i]=1ll*i*jc[i-1]%mmod,ny[i]=1ll*(-mmod/i)*ny[mmod%i]%mmod;
	for(int i=2;i<=n*m;i++) ny[i]=1ll*ny[i]*ny[i-1]%mmod;
	f[0][0]=1;
	for(int i=0;i<=n;i++)
		for(int j=i;j<=n;j++)
		{
			if(i<j) upd(f[i+1][j],f[i][j]);
			upd(f[i][j+1],1ll*f[i][j]*C((j+1)*(m-1)+i-1,m-2)%mmod);
		}
	ans=1ll*f[n][n]*jc[n]%mmod;
	printf("%d\n",(ans+mmod)%mmod);
	return 0;
}