Problem:
Problem Statement

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.

Sample Input 1

2 2

Sample Output 1

4

The following 4 sequences are possible:

(0,1,0,2)

(0,0,1,2)

(0,2,0,1)

(0,0,2,1)

Sample Input 2

3 1

Sample Output 2

1

The following 1 sequence is possible:

(0,0,0)

Sample Input 3

2 3

Sample Output 3

14

Sample Input 4

2000 2000

Sample Output 4

546381702

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <cmath>
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

const int mod=1000000007;
typedef long long ll;

int fac[4000010],inv[4000010],dp[2010][2010];

int power(int x,int y)
{
	int t=1;
	while (y)
	{
		if (y&1) t=ll(t)*x%mod;
		x=ll(x)*x%mod;y>>=1;
	}
	return t;
}

int c(int n,int m)
{
	return ll(fac[n])*inv[m]%mod*inv[n-m]%mod;
}

int main()
{
	//freopen("input.txt","r",stdin);
	//freopen("output.txt","w",stdout);
	int n,k;scanf("%d%d",&n,&k);
	if (k==1) {puts("1");return 0;}
	int M=n*k;
	fac[0]=1;for (int i=1;i<=M;i++) fac[i]=ll(fac[i-1])*i%mod;
	inv[M]=power(fac[M],mod-2);for (int i=M;i;i--) inv[i-1]=ll(inv[i])*i%mod;
	memset(dp,0,sizeof(dp));dp[0][0]=1;
	for (int i=1;i<=n;i++)
		for (int j=0;j<=i;j++)
			dp[i][j]=(ll(dp[i][j-1])*c(M-i-j-(j-1)*(k-2),k-2)+dp[i-1][j])%mod;
	printf("%d\n",ll(dp[n][n])*fac[n]%mod);
	return 0;
}