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<cstdio>
#include<cstring>
#include<algorithm>
#define MAXN 4000
#define MO 924844033
using namespace std;
int dp[MAXN+5][MAXN+5][2],f[MAXN+5];
int n,k,fact[MAXN+5];
bool ed[MAXN+5];
void prepare()
{
	fact[0]=1;
	for(int i=1;i<=MAXN;i++)
		fact[i]=1LL*fact[i-1]*i%MO;
}
int main()
{
//	freopen("captain.in","r",stdin);
//	freopen("captain.out","w",stdout);
	prepare();
	scanf("%d %d",&n,&k);
	int totlen=0;
	ed[0]=true;
	for(int i=1;i<=k;i++)
	{
		totlen+=(n-i)/k+1;
		ed[totlen]=true;
		totlen+=(n-i)/k+1;
		ed[totlen]=true;
	}
	dp[1][0][0]=1;
	for(int i=2;i<=2*n;i++)
		for(int j=0;j<=n;j++)
		{
			dp[i][j][0]=(1LL*dp[i-1][j][0]+1LL*dp[i-1][j][1])%MO;
			if(ed[i-1]==false&&j-1>=0)
				dp[i][j][1]=dp[i-1][j-1][0];
		}
	for(int i=0;i<=n;i++)
		f[i]=(1LL*dp[2*n][i][0]+1LL*dp[2*n][i][1])%MO;
	int ans=0;
	for(int i=0;i<=n;i++)
	{
		if(i%2==0)
			ans=(1LL*ans+1LL*f[i]*fact[n-i]%MO)%MO;
		else
			ans=((1LL*ans-1LL*f[i]*fact[n-i]%MO)+MO)%MO;
	}
	printf("%d\n",ans);
	return 0;
}