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;
typedef long long ll;
ll f[4005][2005][2],ms=924844033,fac[40005],g[40005];
int tot;
bool vis[4005][2],ed[4005];
int main(){
	int n,k;
	scanf("%d%d",&n,&k);
	fac[0]=1;
	for (int i=1;i<=n;i++){
		fac[i]=(fac[i-1]*i)%ms;
		for (int j=0;j<=1;j++){
			int len=0;
			if (!vis[i][j]){
				for (int x=i,y=j;x<=n;x+=k,y^=1){
					vis[x][y]=1; ++len;
				}
				tot+=len;
				ed[tot]=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])%ms;
			if (ed[i]==0) 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])%ms;
	ll ans=fac[n];
	for (int i=1,j=-1;i<=n;i++,j=-j){
		ans=(ans+ms+(j*fac[n-i]*g[i])%ms)%ms;
	}
	printf("%lld\n",ans);
	return 0;
}