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;
#define ll long long
const ll Mod=924844033;
int n,k,tot;
ll f[4010][4010][2];
bool used[2010][2],en[4010];
void upd(ll &x,ll v)
{
	x=(x+v)%Mod;
}
int main()
{
	cin>>n>>k;
	en[0]=true;
	for (int i=1;i<=n;i++)
	{
		for (int j=0;j<2;j++)
		{
			if (used[i][j])
			{
				continue;
			}
			for (int x=i,y=j;x<=n;x+=k,y^=1)
			{
				used[x][y]=true;
				tot++;
			}
			en[tot]=true;
		}
	}
	f[0][0][0]=1;
	for (int i=1;i<=2*n;i++)
	{
		for (int j=0;j<=n;j++)
		{
			f[i][j][0]=(f[i-1][j][0]+f[i-1][j][1])%Mod;
			if (!en[i-1])
			{
				f[i][j+1][1]=f[i-1][j][0];
			}
		}
	}
	ll ans=0,p=1;
	for (int i=n;i>=0;i--)
	{
		p=p*(n-i)%Mod;
		if (n==i)
		{
			p=1;
		}
		ll now=p;
		if (i&1)
		{
			now=(Mod-now)%Mod;
		}
		upd(ans,now*(f[2*n][i][0]+f[2*n][i][1]));
	}
	cout<<ans<<endl;
	return 0;
}