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=2005,P=924844033;
int n,k,f[N],tot,dp[2*N][N][2],s[2*N];
bool vis[2*N],ed[2*N];

int power(int a,int x)
{
	int ans=1;
	for(;x;x>>=1,a=1ll*a*a%P)
		if(x&1)ans=1ll*ans*a%P;
	return ans;
}

int main()
{
	scanf("%d%d",&n,&k);
	for(int i=f[0]=1;i<=n;i++)f[i]=1ll*f[i-1]*i%P;
	for(int i=1;i<=n;i++)
		for(int j=0;j<2;j++)
			if(!vis[2*i+j])
			{
				vis[2*i+j]=true;
				s[++tot]=2*i+j;
				for(int x=i+k,y=j^1;x<=n;x+=k,y^=1)s[++tot]=2*x+y,vis[2*x+y]=true;
				ed[tot]=true;
			}
	dp[1][0][0]=1;
	for(int i=1;i<tot;i++)
		for(int j=0;j<=n;j++)
		{
			dp[i+1][j][0]=(dp[i][j][0]+dp[i][j][1])%P;
			if(j<=n&&!ed[i])dp[i+1][j+1][1]=dp[i][j][0];
		}
	int ans=0;
	for(int i=0,t=1;i<=n;i++,t*=-1)
		ans=(ans+1ll*t*f[n-i]*(dp[tot][i][0]+dp[tot][i][1]))%P;
	printf("%d\n",(ans+P)%P);
	return 0;
}