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;
const int mod=924844033;
int n,m,cnt;
int a[maxn<<1];
ll ans;
ll fac[maxn<<1],g[maxn<<1];
ll f[maxn<<1][maxn<<1][2];
int main()
{
	scanf("%d%d",&n,&m);
	fac[0]=1;for(int i=1;i<=n;i++)fac[i]=(fac[i-1]*i)%mod;
	for(int i=1;i<=m;i++)
	{
		for(int j=i;j<=n;j+=m)a[++cnt]=j;
		for(int j=i;j<=n;j+=m)a[++cnt]=j;	
	}	
	f[1][0][0]=1;
	for(int i=2;i<=cnt;i++)
	{
		for(int j=0;j<=min(i/2,n);j++)
		{
			f[i][j][0]=(f[i-1][j][0]+f[i-1][j][1])%mod;
			if(j>0&&a[i]-a[i-1]==m)f[i][j][1]=f[i-1][j-1][0];	
		}
	} 
	for(int i=0;i<=n;i++)
	{
		g[i]=(f[n<<1][i][0]+f[n<<1][i][1])%mod;
		if(i&1)ans=(ans-g[i]*fac[n-i]%mod+mod)%mod;
		else ans=(ans+g[i]*fac[n-i]%mod)%mod;
	}
	printf("%lld",ans);
	return 0;
}