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 ll long long 
using namespace std;
inline ll read() {
    ll x=0,tmp=1;char ch=getchar();
    while((ch<'0')||(ch>'9')){
        if(ch=='-')tmp=-1;ch=getchar();
    }
    while((ch>='0')&&(ch<='9')){
        x=x*10+ch-'0';ch=getchar(); 
    }
    return x*tmp;
}
ll dp[4005][4005][2];
ll jc[4005];
bool line[4005];
int main(){
    int n=read(),k=read();
    jc[0]=1;
    for(int i=1;i<=n;i++)
    jc[i]=jc[i-1]*i%924844033;
    int tot=0;
    for(int i=1;i<=k;i++)
     for(int t=2;t--;){
         for(int j=i;j<=n;j+=k){
             tot++;
             if(j!=i) line[tot]=1;
         }
     }
    dp[0][0][0]=1;
    for(int i=0;i<=n*2-1;i++)
     for(int j=0;j<=n;j++){
         dp[i+1][j][0]=(dp[i][j][0]+dp[i][j][1])%924844033;
         if(line[i+1]) dp[i+1][j+1][1]=dp[i][j][0];
     }
    ll ans=0;
    for(int i=0,j=1;i<=n;i++,j=-j)
    ans=(ans+((dp[2*n][i][0]+dp[2*n][i][1])*jc[n-i]%924844033)*j+924844033)%924844033;
    cout<<ans;
}