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>
const int mu=924844033;
int n,k,f[2][4005][2],cnt,p[2005],a[4005],now,ans;
int main(){
	scanf("%d%d",&n,&k);
	p[0]=1;
	for(int i=1;i<=n;i++) p[i]=p[i-1]*1ll*i%mu;
	for (int i=1;i<=k;i++){
		a[cnt]=-1;
		for(int j=i;j<=n;j+=k) cnt++;
		a[cnt]=-1;
		for(int j=i;j<=n;j+=k) cnt++;
	}
	now=1,f[now][0][0]=1;
	for (int i=1;i<cnt;i++){
		now=now^1;
		memset(f[now],0,sizeof(f[now]));
		for (int j=0;j<=i;j++){
			f[now][j][0]=(f[now][j][0]+f[now^1][j][1]+f[now^1][j][0])%mu;
			if (j && !a[i]) f[now][j][1]=(f[now][j][1]+f[now^1][j-1][0])%mu;
		}
	}
	ans=p[n];
	for (int i=1;i<=n;i++){
		ans=(ans+(f[now][i][0]+f[now][i][1])*(i&1?-1:1)*1ll*p[n-i]%mu+mu)%mu;
	}
	printf("%d\n",ans);
}