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>
using namespace std;
inline int read()
{
	int t=1,sum=0;char ch=getchar();
	while(ch<'0'||ch>'9')
	{
		if(ch=='-') t=-1;
		ch=getchar();
	}
	while(ch>='0'&&ch<='9')
		sum=sum*10+ch-'0',ch=getchar();
	return t*sum;
}
const int Max=2e3+10,mod=924844033;
int f[Max<<1][Max][2],g[Max],fac[Max],vis[Max][2],a[Max<<1],n,m,tot;
int main()
{
	int i,j,x,y;
	n=read(); m=read();
	for(i=1;i<=n;i++)
		for(j=0;j<2;j++) if(!vis[i][j])
		{
			int len=0;
			for(x=i,y=j;x<=n;x+=m,y^=1)
				vis[x][y]=1,len++;
			tot+=len;
			a[tot]=1;
		}
	f[0][0][1]=1;
	for(i=1;i<=tot;i++)
		for(j=0;j<=i/2;j++)
		{
			f[i][j][0]=(f[i-1][j][0]+f[i-1][j][1])%mod;
			if(j&&!a[i-1])
				f[i][j][1]=f[i-1][j-1][0];
		}
	for(i=0;i<=n;i++) g[i]=(f[tot][i][0]+f[tot][i][1])%mod;
	for(fac[0]=i=1;i<=n;i++) fac[i]=1LL*fac[i-1]*i%mod;
	int ans=0;
	for(i=0;i<=n;i++)
		if(i&1)
			ans=(ans-1LL*g[i]*fac[n-i]%mod)%mod;
		else 
			ans=(ans+1LL*g[i]*fac[n-i]%mod)%mod;
	printf("%d\n",(ans+mod)%mod);
	return 0;
}