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 maxn=4000+10;
const int mod=924844033;
int n,k,fac[maxn],f[maxn][maxn][2],vis[maxn],a[maxn],tot;

int main()
{
	scanf("%d%d",&n,&k);
	fac[0]=1;
	for(int i=1;i<=n;i++) fac[i]=1ll*fac[i-1]*i%mod;
	for(int i=1;i<=k;i++){
		vis[++tot]=1;
		for(int j=i+k;j<=n;j+=k) vis[++tot]=0;
		vis[++tot]=1;
		for(int j=i+k;j<=n;j+=k) vis[++tot]=0;
	}
	f[0][0][0]=1;
	for(int i=1;i<=tot;i++)
		for(int j=0;j<=n;j++){
			f[i][j][0]=(f[i-1][j][0]+f[i-1][j][1])%mod;
			if(j>0&&!vis[i]) f[i][j][1]=f[i-1][j-1][0];
		}
	int ans=0;
	for(int i=0;i<=n;i++){
		if(i&1) ans=(ans-1ll*fac[n-i]*(f[tot][i][0]+f[tot][i][1])%mod+mod)%mod;
		else ans=(ans+1ll*fac[n-i]*(f[tot][i][0]+f[tot][i][1])%mod)%mod;
	}
	printf("%d\n",ans);
	return 0;
}