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 <algorithm>
#define N 4006
#define mo 924844033
using namespace std;
int n,k,t,ans,v[N][2],a[N],g[N],fac[N],f[N][N][2];
int main()
{
	scanf("%d%d",&n,&k);
	for(int i=1;i<=n;i++)
		for(int j=0;j<=1;j++)if(!v[i][j]){
			int len=0;
			for(int x=i,y=j;x<=n;x+=k,y^=1)++len,v[x][y]=1;
			a[t+=len]=1;
		}
	f[0][0][1]=1;
	for(int i=0;i<=t;i++)
		for(int j=0;j<=n;j++){
			f[i+1][j][0]=(f[i][j][0]+f[i][j][1])%mo;
			if(!a[i])f[i+1][j+1][1]=f[i][j][0];
		}
	for(int i=1;i<=n;i++)g[i]=(f[t][i][0]+f[t][i][1])%mo;
	fac[0]=1;for(int i=1;i<=n;i++)fac[i]=1LL*fac[i-1]*i%mo;ans=fac[n];
	for(int i=1,j=-1;i<=n;i++,j=-j)ans=(ans+1LL*j*g[i]%mo*fac[n-i]%mo+mo)%mo;
	printf("%d\n",ans);
}