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> 
#include <algorithm>  
#define ll long long   
#define N 2008  
#define mod 924844033 
#define setIO(s) freopen(s".in","r",stdin) 
using namespace std; 
int f[N<<1][N<<1][2],link[N<<1],fac[N<<1];  
int main() 
{ 
    // setIO("input");  
    int i,j,n,k,tot=0; 
    scanf("%d%d",&n,&k);     
    fac[0]=1,f[0][0][0]=1;    
    for(i=1;i<=n;++i) fac[i]=(ll)fac[i-1]*i%mod;     
    for(i=1;i<=k;++i) 
    {
        for(int t=1;t<=2;++t) 
            for(j=i;j<=n;j+=k) 
                if(j!=i) link[++tot]=1; else ++tot;     
    }    
    for(i=1;i<=tot;++i) 
    {
        for(j=0;j<=n;++j) 
        {   
            f[i][j][0]=(ll)(f[i-1][j][0]+f[i-1][j][1])%mod;    
            if(link[i]) f[i][j][1]=f[i-1][j-1][0];      
        }
    }    
    int ans=0; 
    for(i=0;i<=n;++i) 
    {
        int tmp=(ll)(f[n<<1][i][0]+f[n<<1][i][1])%mod;       
        tmp=(ll)tmp*fac[n-i]%mod;      
        if(i&1) ans=(ll)(ans-tmp+mod)%mod;        
        else ans=(ll)(ans+tmp)%mod;   
    }   
    printf("%d\n",ans); 
    return 0; 
}