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>
#define ll long long
const int N=2005,mo=924844033;
int n,rm,m,i,j,k,f[N][2],ans;
void work(int m,int l,int r){
	if (!m) return;int t=l<=rm;
	for (int i=0;i<=n;i++)
		f[i][t]=(f[i][0]+f[i][1])%mo,f[i][t^1]=0;
	for (int i=1;i<=m;i++){
		for (int j=n;j;j--){
			f[j][0]=((ll)f[j][0]+f[j][1]+f[j-1][0])%mo;
			f[j][1]=(f[j-1][0]+f[j-1][1])%mo;
		}
		f[0][0]=(f[0][0]+f[0][1])%mo;f[0][1]=0;
	}
	if (r<=rm) for (int i=0;i<=n;i++) f[i][1]=0;
}
int main(){
	scanf("%d%d",&n,&m);rm=m;m*=2;
	f[0][0]=1;
	for (i=1;i<=n%m;i++) work(n/m+1,i,n%m-i+1);
	for (i=1;i<=m-n%m;i++)
		work(n/m,m-i+1,n%m+i);
	for (i=0,j=n&1?-1:1,k=1;i<=n;i++,j=-j,k=(ll)k*i%mo)
		ans=(ans+(ll)(f[n-i][0]+f[n-i][1])*k*j)%mo;
	printf("%d",(ans+mo)%mo);
}