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>
using namespace std;
const int maxn=2005,TT=924844033;
int n,m,K,a[maxn];
long long F[maxn][maxn][2],ans;
int main(){
	scanf("%d%d",&n,&K);m=K<<1;
	for (int i=1;i<=m;i++)
	for (int j=i;j<=n;j+=m) a[++a[0]]=j;
	F[0][0][0]=1;
	for (int i=1;i<=n;i++)
	for (int j=0;j<=n;j++){
		F[i][j][0]=F[i-1][j][0]+F[i-1][j][1];
		F[i][j][0]+=(a[i]>K)*(F[i-1][j-1][0]+(a[i]-a[i-1]!=m)*F[i-1][j-1][1]);
		F[i][j][1]=(a[i]+K<=n)*(F[i-1][j-1][0]+F[i-1][j-1][1]);
		F[i][j][0]%=TT,F[i][j][1]%=TT;
	}
	long long fct=1;
	for (int i=n;~i;i--){
		if(n-i) fct=fct*(n-i)%TT;
		ans+=(F[n][i][0]+F[n][i][1])*fct%TT*(i&1?-1:1);
	}
	printf("%lld\n",(ans%TT+TT)%TT);
	return 0;
}