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;
#define ll long long
const int p=1e9+7,N=4010,M=4e6+5;
int dp[N][N],fac[M],finv[M],inv[M];
int comb(int n,int m){return n<m?0:fac[n]*1ll*finv[m]%p*finv[n-m]%p;}
int main()
{
    int n=4e6,k;
    fac[1]=fac[0]=finv[1]=finv[0]=inv[1]=1;
    for(int i=2;i<=n;i++)
        inv[i]=(p-p/i)*1ll*inv[p%i]%p,fac[i]=1ll*fac[i-1]*i%p,
        finv[i]=finv[i-1]*1ll*inv[i]%p;
    cin>>n>>k;
    if(k==1){cout<<1<<endl;return 0;}
    dp[1][0]=1;
    for(int i=1;i<=n;i++)
    {
        for(int j=0;j<=i;j++)
        {
            if(i==1&&j==0)continue;
            dp[i][j]=((j!=i)*dp[i-1][j]+
                     (j!=0)*1ll*comb(n-i+(n-j+1)*(k-1)-1,k-2)*dp[i][j-1])%p;
        }
    }
    printf("%lld\n",1ll*dp[n][n]*fac[n]%p);
}