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=2019,mod=924844033;
int n,k,sum,p,ans,f[2][N][N][2],g[2][N],fac[N];
void add(int&x,int y){x=x+y>=mod?x+y-mod:x+y;}
int main()
{
	scanf("%d%d",&n,&k);
	f[0][0][0][1]=f[1][0][0][0]=1;
	for(int p=0;p<2;p++)
	for(int i=1;i<=n;i++)
	for(int j=0;j<=i;j++)
	{
		add(f[p][i][j][0],f[p][i-1][j][0]);
		add(f[p][i][j][0],f[p][i-1][j][1]);
		if(j)
		{
			add(f[p][i][j][0],f[p][i-1][j-1][0]);
			add(f[p][i][j][1],f[p][i-1][j-1][0]);
			add(f[p][i][j][1],f[p][i-1][j-1][1]);
		}
	}
	g[0][0]=1;
	for(int i=1;i<=2*k&&i<=n;i++)
	{
		int len=(n-i)/k/2+1,tp=i>k;
		p^=1;
		memset(g[p],0,sizeof g[p]);
		if(i+(len-1)*2*k+k>n)
		for(int p1=0;p1<=len;p1++)
		for(int p2=0;p2<=sum;p2++)
		add(g[p][p1+p2],1ll*g[p^1][p2]*f[tp][len][p1][0]%mod);
		else for(int p1=0;p1<=len;p1++)
		for(int p2=0;p2<=sum;p2++)
		add(g[p][p1+p2],1ll*g[p^1][p2]*(f[tp][len][p1][1]+f[tp][len][p1][0])%mod);
		sum+=len;
	}
	fac[0]=1;for(int i=1;i<=n;i++)fac[i]=1ll*fac[i-1]*i%mod;
	for(int i=0;i<=sum;i++)add(ans,1ll*(i&1?mod-1:1)*g[p][i]%mod*fac[n-i]%mod);
	printf("%d",ans);
}