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>

const int N=2040,p=924844033;
int f[N+N][N][2];
bool end[N+N];
int n,k,Ans,fac[N];

inline int qm(int x){return x<p?x:x-p;}

int main(){
	scanf("%d%d",&n,&k);fac[0]=1;
	for(int i=1;i<=n;++i)fac[i]=1ll*fac[i-1]*i%p;
	for(int i=1,tt=0,d;i<=k;++i){
		d=(n-i)/k+1;
		tt+=d,end[tt]=true;
		tt+=d,end[tt]=true;
	}
	f[1][0][0]=1;
	for(int i=1;i<=n+n;++i)
	for(int j=0;j<=n;++j){
		f[i+1][j][0]=qm(f[i][j][0]+f[i][j][1]);
		if(!end[i])f[i+1][j+1][1]=f[i][j][0];
	}
	for(int i=0,t;i<=n;++i){
		t=1ll*fac[n-i]*qm(f[n+n][i][0]+f[n+n][i][1])%p;
		if(i&1)Ans=qm(Ans-t+p);
		else Ans=qm(Ans+t);
	}
	printf("%d\n",Ans);
	return 0;
}