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;
#define ll long long
#define N ((ll)2010)
#define MOD ((ll)1e9+7)
ll tavan(ll x,ll y){ll res=1;while(y){res*=y%2?x:1;res%=MOD;x*=x;x%=MOD;y/=2;}return res;}

ll n,k,fac[N*N],rfac[N*N],dp[N][N];

ll C(ll x,ll y){return (fac[x]*((rfac[y]*rfac[x-y])%MOD))%MOD;}

int main()
{
	cin>>n>>k;
	if(k==1)return cout<<1,0;
	fac[0]=rfac[0]=1;
	for(ll i=1;i<N*N;i++)fac[i]=(fac[i-1]*i)%MOD,rfac[i]=tavan(fac[i],MOD-2);
	dp[0][0]=1;
	for(int i=0;i<=n;i++)
		for(int j=i;j<=n;j++)
		{
			if(i)dp[i][j]=dp[i-1][j];
			if(j>i)dp[i][j]+=dp[i][j-1]*C(j*(k-1)+i-1,k-2);
			dp[i][j]%=MOD;
		}
	cout<<(dp[n][n]*fac[n])%MOD;
	return 0;
}