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 ll long long
using namespace std;
const int maxn=2000+10;
const int p=1e9+7;
int n,k,f[maxn][maxn],farc[maxn*maxn],inv[maxn*maxn];

int C(int n,int m){
	return (ll)farc[n]*inv[m]%p*(ll)inv[n-m]%p;
}

int main()
{
	scanf("%d%d",&n,&k);k--;
	if(!k){printf("1\n");return 0;}
	farc[0]=farc[1]=inv[0]=inv[1]=1;
	for(int i=2;i<=n*k+n+k;i++){
		farc[i]=(ll)farc[i-1]*i%p;
		inv[i]=(ll)(p-p/i)*inv[p%i]%p;
	}
	for(int i=2;i<=n*k+n+k;i++) inv[i]=(ll)inv[i]*inv[i-1]%p;
	f[0][0]=1;
	for(int i=0;i<=n;i++)
		for(int j=i;j<=n;j++){
			if(i>0) f[i][j]=(f[i][j]+f[i-1][j])%p;
			if(j>0) f[i][j]=(f[i][j]+(ll)f[i][j-1]*C(i+(j-1)*k+k-1,k-1)%p)%p;
		}
	printf("%d\n",(ll)f[n][n]*farc[n]%p);
	return 0;
}