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;
const int maxn=2010,maxm=maxn<<1;
#define mod 924844033
int vis[maxn][2],ed[maxm];
int tot;LL f[maxm][maxn][2],fac[maxn];
int main(){
	int n,k;
	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][1]+f[i][j][0])%mod;
			if(!ed[i])f[i+1][j+1][1]=f[i][j][0];
		}	
	}
	fac[0]=1;
	for(LL i=1;i<=n;++i)fac[i]=fac[i-1]*i%mod;
	LL ans=fac[n];
	for(LL i=1,j=-1;i<=n;++i,j=-j){
/**/	ans=(ans+mod+j*fac[n-i]*((f[tot][i][0]+f[tot][i][1])%mod)%mod)%mod;
	}
	cout<<ans<<endl;
	return 0;
}