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<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#define Mod 1000000007
using namespace std;
long long f[2010][2010];
int n,k;
long long fac[4000010],inv[4000010];
long long fpow(long long a,long long b)
{
	long long ans=1,t=a;
	while(b)
	{
		if(b&1)ans=ans*t%Mod;
		t=t*t%Mod;
		b>>=1;
	}
	return ans;
}
void getfac()
{
	fac[0]=1;
	for(int i=1;i<=n*k;i++)
		fac[i]=fac[i-1]*i%Mod;
	inv[n*k]=fpow(fac[n*k],Mod-2);
	for(int i=n*k;i;i--)
		inv[i-1]=inv[i]*i%Mod;
	return ;
}
long long C(int a,int b)
{
	return fac[a]*inv[b]%Mod*inv[a-b]%Mod;
}
int main()
{
	cin>>n>>k;
	if(k==1){
		cout<<1<<"\n";
		return 0;
	}
	getfac();
	f[0][0]=1;
	for(int i=1;i<=n;i++)
		for(int j=0;j<=i;j++)
		{
			f[i][j]+=f[i-1][j];
			if(j)
				f[i][j]=(f[i][j]+f[i][j-1]*(n-j+1)%Mod*C(n-i+(k-1)*(n-j+1)-1,k-2)%Mod)%Mod;
		}
	printf("%lld\n",f[n][n]);
	return 0;
}