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>
#define cal(a,b) ((a+=b)%=mo)
using namespace std;
const int N=2050,mo=924844033;
int f[N][N][2][2],a[N],tot,p[N];
int main(){
  int n,k; cin>>n>>k;
  for (int i=1; i<=k; ++i)
    for (int j=i; j<=n; j+=k)
      a[++tot]=j;
  f[0][0][0][0]=1; a[0]=n;
  for (int i=0; i<n; ++i)
    for (int j=0; j<=i; ++j)
      for (int t=0; t<=1; ++t){
	cal(f[i+1][j+1][t][0],f[i][j][0][t]*(a[i+1]-a[i]==k));
	cal(f[i+1][j+1][t][1],((f[i][j][0][t]+f[i][j][1][t])%mo)*(a[i+2]-a[i+1]==k));
	cal(f[i+1][j][t][0],(f[i][j][0][t]+f[i][j][1][t])%mo);
      }
  p[0]=1;
  for (int i=1; i<=n; ++i) p[i]=1ll*p[i-1]*i%mo;
  for (int i=0; i<=n; ++i)
    cal(f[n][i][0][0],f[n][i][1][0]);
  int ans=0;
  for (int i=0; i<=n; ++i)
    if (i&1) cal(ans,mo-1ll*p[n-i]*f[n][i][0][0]%mo);
    else cal(ans,1ll*p[n-i]*f[n][i][0][0]%mo);
  cout<<ans;
  return 0;
}