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>
typedef long long ll;
const int N=2003,M=924844033;
int n,m,fac[N],f[N+N][N],t,a[N+N],ans;
int main(){
	scanf("%d%d",&n,&m);
	fac[0]=1;
	for(int i=1;i<=n;i++)fac[i]=(ll)fac[i-1]*i%M;
	a[t=0]=1;
	for(int i=1;i<=(n-m)%m;i++)
	  a[t+=(n-m)/m+1]=1,a[t+=(n-m)/m+1]=1;
	for(int i=1;i<=m-(n-m)%m;i++)
	  a[t+=(n-m)/m]=1,a[t+=(n-m)/m]=1;
	f[0][0]=1;
	for(int i=1;i<=t;i++)
	  for(int j=0;j<=n;j++)
		f[i][j]=(f[i-1][j]+(j?f[i-1-(!a[i-1])][j-1]:0))%M;
	for(int j=0;j<=n;j++)
	  ans=(ans+(ll)f[t][j]*fac[n-j]%M*(j&1?M-1:1))%M;
	printf("%d\n",ans);
	return 0;
}