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=4010,mod=924844033;
int n,K,f[N][N][2],g[N],Fac[N];bool vis[N][2],d[N];
int main(){
  scanf("%d%d",&n,&K);
  int tot=0;
  for(int i=1;i<=n;i++){
	  for(int j=0;j<2;j++){
		  if(vis[i][j])continue;
		  int t=0;
		  for(int x=i,y=j;x<=n;x+=K,y^=1)vis[x][y]=1,t++;
		  d[tot+=t]=1;
	  }
  }
  f[0][0][1]=1;
  for(int i=0;i<tot;i++){
	  for(int j=0;j<=i;j++){
		  f[i+1][j][0]=(1ll*f[i+1][j][0]+f[i][j][0]+f[i][j][1])%mod;
		  if(!d[i])f[i+1][j+1][1]=(f[i+1][j+1][1]+f[i][j][0])%mod;
	  }
  }
  for(int i=1;i<=n;i++)
	  g[i]=(f[tot][i][0]+f[tot][i][1])%mod;
  Fac[0]=1;
  for(int i=1;i<=n;i++)Fac[i]=1ll*Fac[i-1]*i%mod;
  int ans=Fac[n];
  for(int i=1;i<=n;i++)ans=(ans+1ll*(i&1?-1:1)*g[i]*Fac[n-i])%mod;
  if(ans<0)ans+=mod;
  cout<<ans<<endl;
  return 0;
}