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<algorithm>
#include<iostream>
#include<cstring>
using namespace std;
typedef long long LL;
const int N=2005;
const int MOD=924844033;
int n,m;
bool ok[N*2];
int tot=0;
int f[N*2][N][2];
int JC[N];
int add (int x,int y)	{x=x+y;if (x>=MOD) x-=MOD;return x;}
int mul (int x,int y)	{return (LL)x*y%MOD;}
int dec (int x,int y)	{x=x-y;if (x<0) x=x+MOD;return x;}
int main()
{
	memset(ok,false,sizeof(ok));
	scanf("%d%d",&n,&m);
	JC[0]=1;for (int u=1;u<=n;u++) JC[u]=mul(JC[u-1],u);
	for (int u=1;u<=m;u++)
		for (int i=u;i<=n;i+=m)
		{
			tot++;
			if (u!=i) ok[tot]=true;
		}
	for (int u=1;u<=m;u++)
		for (int i=u;i<=n;i+=m)
		{
			tot++;
			if (u!=i) ok[tot]=true;
		}
	f[0][0][0]=1;
	for (int u=1;u<=tot;u++)
		for (int i=0;i<=n;i++)
		{
			f[u][i][0]=add(f[u-1][i][1],f[u-1][i][0]);
			if (ok[u+1]&&i>0) f[u][i][1]=f[u-1][i-1][0];
		}
	int ans=0;
	for (int u=0;u<=n;u++)
	{
		if (u&1) ans=dec(ans,mul(add(f[tot][u][1],f[tot][u][0]),JC[n-u]));
		else ans=add(ans,mul(add(f[tot][u][1],f[tot][u][0]),JC[n-u]));
	}
	printf("%d\n",ans);
	return 0;
}