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<bits/stdc++.h>
using namespace std;
const int mo=924844033;
const int N=4005;
int n,k,tot;
int ed[N],vis[N][2];
int f[N][N][2];
int g[N],fac[N];
int main(){
	scanf("%d%d",&n,&k);
	for (int i=1;i<=n;i++)
		for (int j=0;j<=1;j++)
			if (!vis[i][j]){
				int len=0;
				for (int x=i,y=j;x<=n;x+=k,y^=1)
					vis[x][y]=1,++len;
				ed[tot+=len]=1;
			}
	f[1][0][0]=1;
	for (int i=1;i<=tot;i++)
		for (int j=0;j<=n;j++){
			f[i+1][j][0]=(f[i][j][0]+f[i][j][1])%mo;
			if (!ed[i]) f[i+1][j+1][1]=f[i][j][0];
		}
	for (int i=0;i<=n;i++)
		g[i]=(f[tot][i][0]+f[tot][i][1])%mo;
	fac[0]=1;
	for (int i=1;i<=n;i++)
		fac[i]=1ll*fac[i-1]*i%mo;
	int ans=fac[n];
	for (int i=1,j=mo-1;i<=n;i++,j=mo-j)
		ans=(ans+1ll*j*fac[n-i]%mo*g[i]%mo)%mo;
	printf("%d",ans);
}