Problem: Snuke loves permutations. He is making a permutation of length N.

Since he hates the integer K, his permutation will satisfy the following:

* Let the permutation be a_1, a_2, ..., a_N. For each i = 1,2,...,N, |a_i - i| \neq K.



Among the N! permutations of length N, how many satisfies this condition?

Since the answer may be extremely large, find the answer modulo 924844033(prime).

Constraints

* 2 ≦ N ≦ 2000
* 1 ≦ K ≦ N-1

Input

The input is given from Standard Input in the following format:


N K


Output

Print the answer modulo 924844033.

Examples

Input

3 1


Output

2


Input

4 1


Output

5


Input

4 2


Output

9


Input

4 3


Output

14


Input

425 48


Output

756765083

Solution (in CPP):

Solution:
#include <iostream>
#include <cstdio> 
#include <cstring>
using namespace std;
#define MOD 924844033
#define ll long long
#define N 2050
ll dp[N<<1][N][2],n,k,link[2*N],tot,sum,jc[N];
int main()
{
	scanf("%lld%lld",&n,&k);
	jc[0]=1;dp[0][0][0]=1;
	for(int i=1;i<=n;i++)jc[i]=jc[i-1]*i%MOD; 
	for(int i=1;i<=k;i++)
		for(int t=1;t<=2;t++)
			for(int j=i;j<=n;j+=k)
				j!=i?link[++tot]=1:++tot;
	for(int i=1;i<=tot;i++)
		for(int j=0;j<=n;j++)
		{
			dp[i][j][0]=(dp[i-1][j][1]+dp[i-1][j][0])%MOD;
			if(link[i])dp[i][j][1]=dp[i-1][j-1][0];
	 	}
	for(int i=0;i<=n;i++)
	{
		ll tmp=(dp[n<<1][i][0]+dp[n<<1][i][1])%MOD;
		tmp=tmp*jc[n-i]%MOD;
		i%2==1?sum=((sum-tmp)%MOD+MOD)%MOD:sum=(sum+tmp)%MOD;
	}
	printf("%lld",sum);
	return 0;
}