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 MOD 1000000007
using namespace std;
inline int add(int a,int b)
{a+=b;return a>=MOD?a-MOD:a;}
inline int mul(int a,int b)
{return 1LL*a*b%MOD;}
int ksm(int a,int b)
{
	int ans=1;
	for(;b;b>>=1,a=mul(a,a))
		if(b&1)ans=mul(ans,a);
	return ans;
}
const int Q=2005;
int fac[Q*Q],ifac[Q*Q];
int F(int n,int m)
{return mul(fac[n+m-1],mul(ifac[m-1],ifac[n]));}
void Init(int n)
{
	fac[0]=1;
	for(int i=1;i<=n;i++)
		fac[i]=mul(fac[i-1],i);
	ifac[n]=ksm(fac[n],MOD-2);
	for(int i=n;i;--i)
		ifac[i-1]=mul(ifac[i],i);
}
int f[Q][Q];
int main()
{
	int n,k;
	scanf("%d%d",&n,&k);
	if(k==1)return 0&puts("1");
	Init(n*k);
	f[0][0]=1;
	for(int i=1;i<=n;i++)
		for(int j=i;j>=0;--j)
			f[i][j]=add(f[i][j+1],j==0?0:mul(f[i-1][j-1],mul(n-i+1,F(k-2,(i-1)*k-(j-1)+1))));
	printf("%d\n",f[n][0]);
	return 0;
}