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;
#define RI register int
const int mod=924844033,N=4005;
int vis[N][2],ed[N],f[N][N][2],fac[N],js,n,K,ans;
int qm(int x) {return x>=mod?x-mod:x;}
int main()
{
	scanf("%d%d",&n,&K);
	for(RI i=1;i<=n;++i)
		for(RI j=0;j<=1;++j) {
			if(vis[i][j]) continue;
			for(RI x=i,y=j;x<=n;x+=K,y^=1) ++js,vis[x][y]=1;
			ed[js]=1;
		}
	f[1][0][0]=1;
	for(RI i=1;i<=js;++i)
		for(RI j=0;j<=n;++j) {
			f[i+1][j][0]=qm(f[i][j][0]+f[i][j][1]);
			if(!ed[i]) f[i+1][j+1][1]=f[i][j][0];
		}
	fac[0]=1;for(RI i=1;i<=n;++i) fac[i]=1LL*fac[i-1]*i%mod;
	for(RI i=0,fh=1;i<=n;++i,fh=-fh)
		ans=qm(ans+qm(1LL*fh*qm(f[js][i][0]+f[js][i][1])%mod*fac[n-i]%mod+mod));
	printf("%d\n",ans);
	return 0;
}