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 N=4010,mod=924844033;
int n,k,tot,ans,vis[N][2],fac[N],ed[N],g[N],f[N][N][2];
int main()
{
	scanf("%d%d",&n,&k);
	for(int i=fac[0]=1;i<=n;i++)fac[i]=1ll*fac[i-1]*i%mod;
	for(int i=1;i<=n;i++)for(int j=0;j<2;j++)if(!vis[i][j]){int l=0;for(int x=i,y=j;x<=n;x+=k,y^=1)vis[x][y]=1,l++;ed[tot+=l]=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])%mod;
		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])%mod;
	for(int i=0,j=1;i<=n;i++,j=mod-j)ans=(ans+1ll*j*fac[n-i]%mod*g[i])%mod;
	printf("%d\n",ans);
	return 0;
}