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<cstdio>
#define MN 2000
#define MX 4000000
#define mod 1000000007
using namespace std;
inline int read()
{
	int x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}
int f[MN+5][MN+5],n,k,p[MX+5],inv[MX+5];
inline void R(int&x,int y){x+=y;x>=mod?x-=mod:0;}
inline int C(int n,int m){return 1LL*p[n]*inv[m]%mod*inv[n-m]%mod;}
int main()
{
	n=read();k=read();if(k==1) return 0*puts("1");
	p[0]=inv[0]=p[1]=inv[1]=f[0][0]=1;
	for(int i=2;i<=n*k;++i) p[i]=1LL*p[i-1]*i%mod,inv[i]=1LL*(mod-mod/i)*inv[mod%i]%mod;
	for(int i=2;i<=n*k;++i) inv[i]=1LL*inv[i]*inv[i-1]%mod;
	for(int i=0;i<=n;++i)
		for(int j=0;j<=i;++j)
		{
			if(i<n) R(f[i+1][j],f[i][j]);
			if(j<i) R(f[i][j+1],1LL*f[i][j]*C((n-j-1)*(k-1)+n-i+k-1-1,k-2)%mod*(n-j)%mod);	
		}
	printf("%d\n",f[n][n]);
	return 0;
}