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<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=4009;
const int md=924844033;
int n,k;
bool vis[N][N];
int ed[N],tot;
int f[N][N][2];
int g[N],fac[N];
int main() {
	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][0]+f[i][j][1])%md;
			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])%md;
	fac[0]=1;
	for(int i=1;i<=n;i++) fac[i]=(ll)fac[i-1]*i%md;
	int ans=fac[n];
	for(int i=1,j=-1;i<=n;i++,j=-j) 
		ans=((ll)ans+md+(ll)j*fac[n-i]*g[i]%md)%md;
	printf("%lld\n",ans);
	return 0;
}