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
#define MOD 1000000007
using namespace std;
int N,K;
LL fac[5000010],inv[5000010],ifac[5000010],d[2010][2010];
int main()
{
	cin>>N>>K;
	if(K==1)
	{
		cout<<1<<endl;
		return 0;
	}
	fac[0]=inv[0]=ifac[0]=fac[1]=inv[1]=ifac[1]=1;
	for(int i=2;i<=5000000;i++)
	{
		fac[i]=(fac[i-1]*i)%MOD;
		inv[i]=inv[MOD%i]*(MOD-MOD/i)%MOD;
		ifac[i]=(ifac[i-1]*inv[i])%MOD;
	}
	d[0][1]=1;
	for(int i=2;i<=N;i++)
	{
		d[0][i]=d[0][i-1]*(fac[i*(K-1)-1]*ifac[K-2]%MOD*ifac[(i-1)*(K-1)]%MOD)%MOD;
	}
	for(int i=1;i<=N;i++)
	{
		for(int j=i;j<=N;j++)
		{
			d[i][j]=(d[i-1][j]+d[i][j-1]*(fac[i+j*(K-1)-1]*ifac[K-2]%MOD*ifac[i+(j-1)*(K-1)]%MOD))%MOD;
// 			cout<<i<<' '<<j<<' '<<d[i][j]<<endl;
		}
	}
	cout<<(d[N][N]*fac[N])%MOD<<endl;
	return 0;
}