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;
typedef long long ll;
const int N=2010,p=1e9+7;
int inc(int x,int y){x+=y;return x>=p?x-p:x;}
int mul(int x,int y){return (ll)x*y%p;}
int power(int x,int y){
	int ans=1;
	for (;y;y>>=1,x=mul(x,x))
		if (y&1) ans=mul(ans,x);
	return ans;
}
int n,k,dp[N][N],fac[N*N],ifac[N*N];
int C(int n,int m){
	return mul(fac[n],mul(ifac[m],ifac[n-m]));
}
int main()
{
	cin>>n>>k;
	if (k==1) return puts("1"),0;
	fac[0]=1;
	for (int i=1;i<=n*k;i++) fac[i]=mul(fac[i-1],i);
	ifac[n*k]=power(fac[n*k],p-2);
	for (int i=n*k;i;i--) ifac[i-1]=mul(ifac[i],i);
	dp[0][0]=1;
	for (int i=0;i<=n;i++)
	for (int j=0;j<=n;j++){
		if (i) dp[i][j]=inc(dp[i][j],dp[i-1][j]);
		if (i!=j&&j) dp[i][j]=inc(dp[i][j],mul(dp[i][j-1],C(i+j*(k-1)-1,k-2)));
	}
	printf("%d\n",mul(fac[n],dp[n][n]));
	return 0;
}