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>
using namespace std;
const int md=1000000007;
int f[2010][2010],fac[4000010],inv[4000010],rev[4000010];
int c(int n,int m){return 1ll*fac[n]*rev[m]%md*rev[n-m]%md;}
int main()
{
    int n,k;
    cin>>n>>k;
    if(k==1){puts("1");return 0;}
    f[0][0]=1;
    fac[0]=fac[1]=1,inv[1]=1,rev[0]=rev[1]=1;
    for(int i=2;i<=n*k;i++)
	{
		fac[i]=1ll*fac[i-1]*i%md;
		inv[i]=1ll*(md-md/i)*inv[md%i]%md;
		rev[i]=1ll*rev[i-1]*inv[i]%md;
	}
	for(int i=1;i<=n;i++)for(int j=i;j>=0;j--)
	{
	    f[i][j]=f[i][j+1];
	    if(j)f[i][j]=(f[i][j]+1LL*f[i-1][j-1]*c(i*k-j-1,k-2)%md)%md;
	}
    cout<<1LL*f[n][0]*fac[n]%md<<endl;
    return 0;
}