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 <cmath>
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <queue>
#include <map>
#include <bitset>
#include <set>
const int inf=2147483647;
const int mo=924844033;	
const int N=4005;
using namespace std;
int n,m,tot;
bool lk[N];
long long f[N][N][2],jc[N],ans;
int main()
{
	//freopen("agc005d.in","r",stdin);
	//freopen("agc005d.out","w",stdout);
	scanf("%d%d",&n,&m);
	jc[0]=1;
	for(int i=1;i<=n;i++) jc[i]=1ll*jc[i-1]*i%mo;
	for(int i=1;i<=m;i++)
		for(int t=2;t--;)
			for(int j=i;j<=n;j+=m)
			{
				tot++;
				if(j!=i) lk[tot]=1;
			}
	f[0][0][0]=1;
	for(int i=0;i<n*2;i++)
		for(int j=0;j<=n;j++)
		{
			f[i+1][j][0]=(f[i][j][0]+f[i][j][1])%mo;
			if(lk[i+1]) f[i+1][j+1][1]=f[i][j][0];
		}
	for(int i=0,t=1;i<=n;i++,t=-t)
	{
		f[2*n][i][0]=1ll*(f[2*n][i][0]+f[2*n][i][1])*jc[n-i]%mo;
		ans=(ans+f[2*n][i][0]*t+mo)%mo;
	}
	printf("%lld\n",ans);
}