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;
const int N=2050,mod=924844033;
int n,m,k,ans,jc[N]= {1},f[N*2][N][2];
bool ed[N],vis[N][2];
int main()
{
	scanf("%d%d",&n,&k);
	for(int i=1; i<=n; i++)
		for(int j=0; j<2; j++)
			if(!vis[i][j])
			{
				int cnt=0;
				for(int x=i,y=j; x<=n; x+=k,y^=1)
				{
					cnt++;
					vis[x][y]=true;
				}
				m+=cnt;
				ed[m]=true;
			}
	f[1][0][0]=1;
	for(int i=1; i<=m; i++)
		for(int j=0; j<=n; j++)
		{
			f[i+1][j][0]=f[i][j][0]+f[i][j][1]<mod?f[i][j][0]+f[i][j][1]:f[i][j][0]+f[i][j][1]-mod;
			if(!ed[i])
				f[i+1][j+1][1]=f[i][j][0];
		}
	for(int i=1; i<=n; i++)
		jc[i]=1LL*jc[i-1]*i%mod;
	ans=jc[n];
	for(int i=1; i<=n; i++)
		if(i&1)
			ans=(ans-1LL*(f[m][i][0]+f[m][i][1])%mod*jc[n-i]%mod+mod)%mod;
		else
			ans=(ans+1LL*(f[m][i][0]+f[m][i][1])%mod*jc[n-i]%mod)%mod;
	printf("%d\n",ans);
}