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<cstdio>
#include<cstring>
#include<algorithm>
#include<vector>
#define SF scanf
#define PF printf
#define MAXN 2010
#define MOD 1000000007
using namespace std;
typedef long long ll;
ll dp[MAXN][MAXN];
ll fac[MAXN*MAXN+MAXN*2],inv[MAXN*MAXN+MAXN*2];
ll fsp(ll x,int y){
	ll res=1;
	while(y){
		if(y&1)
			res=res*x%MOD;
		x=x*x%MOD;
		y>>=1;
	}
	return res;
}
ll C(int x,int y){
	return fac[x]*inv[y]%MOD*inv[x-y]%MOD;	
}
int n,k;
int main(){
	fac[0]=1;
	for(int i=1;i<=4004000;i++)
		fac[i]=fac[i-1]*i%MOD;
	inv[4004000]=fsp(fac[4004000],MOD-2);
	for(int i=4004000;i>0;i--)
		inv[i-1]=inv[i]*i%MOD;
	SF("%d%d",&n,&k);
	if(k==1){
		PF("1");
		return 0;
	}
	k--;
	dp[0][0]=1;
	for(int i=0;i<=n;i++)
		for(int j=i;j<=n;j++){
			if(i!=0)
				dp[i][j]=(dp[i][j]+dp[i-1][j])%MOD;
			if(j!=0)
				dp[i][j]=(dp[i][j]+dp[i][j-1]*C(i+(j-1)*k+k-1,k-1)%MOD)%MOD;
		}
	PF("%lld",dp[n][n]*fac[n]%MOD);
}