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 N 10000005
using namespace std;
const int p = 1000000007;
int n,k;
int jie[N],ni[N];
int c(int x,int y)
{
    return 1LL*jie[x]*ni[y]%p*ni[x-y]%p;
}
int f[2005][2005];
int main()
{
    jie[0]=ni[0]=ni[1]=1;
    for(int i=1;i<=10000000;i++)jie[i]=1LL*jie[i-1]*i%p;
    for(int i=2;i<=10000000;i++)ni[i]=1LL*(p-p/i)*ni[p%i]%p;
    for(int i=2;i<=10000000;i++)ni[i]=1LL*ni[i-1]*ni[i]%p;
    scanf("%d%d",&n,&k);
    if(k==1)return puts("1"),0;
    f[0][0]=1;
    for(int i=0;i<=n;i++)
    {
        //cout<<i<<endl;
        for(int j=n;j>=0;j--)
        {
           // cout<<i<<' '<<j<<endl;
            (f[i+1][j+1]+=1LL*f[i][j]*c((i+1)*k-j-2,k-2)%p)%=p;
            if(j)(f[i][j-1]+=f[i][j])%=p;
        }
    }
    int ans=1LL*f[n][0]*jie[n]%p;
    printf("%d\n",ans);
    return 0;
}