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 <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
const int N=4000010,Mo=1000000007;
int f[2010][2010],fac[N],inv[N],rev[N];
inline int C(int n,int m) {
    return 1LL*fac[n]*rev[m]%Mo*rev[n-m]%Mo;
}
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%Mo;
	inv[i]=1LL*(Mo-Mo/i)*inv[Mo%i]%Mo;
	rev[i]=1LL*rev[i-1]*inv[i]%Mo;
    }
    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]+=1LL*f[i-1][j-1]*C(i*k-j-1,k-2)%Mo)%=Mo;
	}
    cout<<1LL*f[n][0]*fac[n]%Mo;
    return 0;
}