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<cstdio>
#include<cstring>
#include<algorithm>
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define N 2050
#define mo 924844033
#define ll long long
using namespace std;
int n,m,bz[N+N],a[N][N],tot=0;
ll f[N+N][N][2],jc[N],g[N],ans;
int main()
{
	scanf("%d%d",&n,&m);
	jc[0]=1;
	fo(i,1,n) jc[i]=(jc[i-1]*(ll)i)%mo;
	fo(i,1,n)
	{
		fo(j,0,1)
		if(a[i][j]==0)
		{
			int ed=0;
			for(int x=i,y=j;x<=n;x+=m,y^=1) a[x][y]=1,ed++;
			bz[tot+=ed]=1;
		}
	}
	f[1][0][0]=1;
	fo(i,1,tot)
	{
		fo(j,0,n)
		{
			f[i+1][j][0]=(f[i][j][1]+f[i][j][0])%mo;
			if(!bz[i]) f[i+1][j+1][1]=f[i][j][0]; 
		}
	}
	fo(i,0,n) g[i]=(f[tot][i][0]+f[tot][i][1])%mo;
	ans=jc[n];
	ll j=-1;
	fo(i,1,n)
	{
		ans=(ans+g[i]*jc[n-i]*j%mo+mo)%mo;
		j=-j;
	}
	printf("%lld\n",ans);
}