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<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
#define lol(i,n) for(int i=0;i<n;i++)
#define mod 924844033
#define mad(a,b) a=(a+b)%mod;
#define N 2010
ll f[N],g[N],fc[N],gc[N],n,k;
void solve(ll m){
    for(int i=0;i<m-1;i++){
     lol(j,N)fc[i]=gc[i]=0;
     lol(j,N-1){
         fc[j+1]=g[j];
         gc[j]=(f[j]+g[j])%mod;
     }
     lol(j,N)f[j]=fc[j],g[j]=gc[j];
    }
    lol(j,N){
        mad(g[j],f[j]);
        f[j]=0;
    }
}
int main(){
    lol(i,N)f[i]=g[i]=0;g[0]=1;
    cin>>n>>k;
    for(ll a=0;a<k;a++){
        solve((n+k-1-a)/k);
        solve((n+k-1-a)/k);
    }
    ll fac[N]; fac[0]=1;
    for(ll i=1;i<N;i++)fac[i]=fac[i-1]*i%mod;
    ll ans=0;
    for(ll i=0;i<=n;i++){
        ll val=(i%2==0?+1:-1);
        mad(ans,val*g[i]*fac[n-i]);
    }
    if(ans<0)ans+=mod;
    cout<<ans<<endl;
 return 0;   
}