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 mo=924844033;
int f[4005][2005][2];
bool u[4005];
int main(){
	int n,k;
	scanf("%d%d\n",&n,&k);
	int x=(n-1)/k+1,y=0;
	for (int i=((n-1)%k+1)*2;i;i--) u[y+=x]=1;
	for (;y<2*n;) u[y+=x-1]=1;
	f[0][0][1]=1;
	for (int i=1;i<=2*n;i++)
		for (int j=0;j<=n;j++){
			f[i][j][0]=f[i][j][1]=f[i-1][j][1];
			if (!u[i-1] && j) (f[i][j][1]+=f[i-1][j-1][0])%=mo;
		}
	int ans=0;
	for (int i=0,j=(n&1)?-1:1,k=1;i<=n;j=-j,k=1ll*k*++i%mo)
		ans=(ans+1ll*f[2*n][n-i][1]*k*j)%mo;
	printf("%d\n",(ans+mo)%mo);
}