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<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
const int Mod=1e9+7;
int fac[4110000],ifac[4110000],f[2100][2100],n,k;

int pow(int x,int l){
	if(l==0)return 1;
	int t=pow(x,l/2);
	t=(ll)t*t%Mod;
	if(l&1)t=(ll)t*x%Mod;
	return t;
}

int C(int x,int y){
	return (ll)fac[x]*ifac[y]%Mod*ifac[x-y]%Mod;
}

int main(){
	scanf("%d %d",&n,&k);
	if(k==1){
		printf("%d\n",1);
		return 0;
	}
	fac[0]=1;for(int i=1;i<=4099999;i++)fac[i]=(ll)fac[i-1]*i%Mod;
	ifac[4099999]=pow(fac[4099999],Mod-2);for(int i=4099998;i>=0;i--)ifac[i]=(ll)ifac[i+1]*(i+1)%Mod;
	f[0][0]=1;
	for(int i=1;i<=n;i++)
		f[0][i]=(ll)f[0][i-1]*C(0+i*(k-1)-1,k-2)%Mod;
	for(int i=1;i<=n;i++){
		f[i][i]=f[i-1][i];
		for(int j=i+1;j<=n;j++){
			f[i][j]=(f[i-1][j]+(ll)f[i][j-1]*C(i+j*(k-1)-1,k-2))%Mod;
		}
	}
	printf("%d\n",(ll)f[n][n]*fac[n]%Mod);
	return 0;
}