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>

const long long mod=924844033ll;

void ad(long long &a,long long b){a+=b;a%=mod;}

int main()
{
  int n,K;
  scanf("%d%d",&n,&K);
  static long long M[2][2001][2]={0};
  bool b=0;
  M[b][0][0]=1ll;
  for(int i=0;i<2*K;i++){
    for(int j=i;j<n;j+=2*K){
      for(int k=0;k<=n;k++){
	if(k+1<=n&&K<=j){
	  ad(M[!b][k+1][0],M[b][k][0]);
	}
	if(k+1<=n&&j+K<n){
	  ad(M[!b][k+1][1],M[b][k][0]);
	  ad(M[!b][k+1][1],M[b][k][1]);
	}
	ad(M[!b][k][0],M[b][k][0]);
	ad(M[!b][k][0],M[b][k][1]);
	M[b][k][0]=M[b][k][1]=0ll;
      }
      b=!b;
    }
    for(int k=0;k<=n;k++){
      ad(M[b][k][0],M[b][k][1]);
      M[b][k][1]=0;
    }
  }
  static long long P[2001];
  P[0]=1ll;
  for(int k=1;k<=n;k++){
    P[k]=P[k-1]*k%mod;
  }
  long long ans=0ll;
  for(int k=0;k<=n;k++){
    //printf("%lld %lld %lld\n",M[b][k][0],P[n-k],ans);
    ad(ans,M[b][k][0]*P[n-k]%mod*(k%2==0?1:mod-1)%mod);
  }
  printf("%lld\n",ans);
  return 0;
}