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<bits/stdc++.h>
using namespace std;
#define LL long long
#define update(a,b) (a)+=(b),(a)=(a)<mo?(a):(a)-mo

const int maxn=2010;
const int mo=924844033;

int n,K,Ans,fac[maxn],dp[maxn][2],tmp[maxn][2];

int main()
{
#ifdef h10
	freopen("D.in","r",stdin);
	freopen("D.out","w",stdout);
#endif
	int o,i,j;
	scanf("%d%d",&n,&K);
	fac[0]=1;
	for (i=1;i<=n;i++)
		fac[i]=(LL)fac[i-1]*i%mo;

	memset(dp,0,sizeof(dp));
	dp[0][0]=1;
	for (o=1;o<=2*K;o++)
	{
		for (i=o;i<=n;i+=2*K)
		{
			memset(tmp,0,sizeof(tmp));
			for (j=0;j<n;j++)
			{
				update(tmp[j][0],dp[j][0]);
				update(tmp[j][0],dp[j][1]);
				if (i>K) update(tmp[j+1][0],dp[j][0]);
				if (i+K<=n)
				{
					update(tmp[j+1][1],dp[j][0]);
					update(tmp[j+1][1],dp[j][1]);
				}
			}
			memcpy(dp,tmp,sizeof(tmp));
		}
		for (i=0;i<=n;i++)
			update(dp[i][0],dp[i][1]),dp[i][1]=0;
	}

	Ans=0;
	for (i=0;i<=n;i++)
	{
		int val=(LL)dp[i][0]*fac[n-i]%mo;
		update(Ans,(i&1)?mo-val:val);
	}
	printf("%d\n",Ans);
}