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<cstdio>
using namespace std;
 
#define mod 924844033
int n,k,tot=0,fac[2005];
int g[2005],f[4005][4005][2];
bool vis[2005][2],End[4005];
 
int main(){
    scanf("%d%d",&n,&k);
    for(int i=1;i<=n;i++)
    for(int j=0;j<=1;j++)
        if(!vis[i][j]){
           for(int a=i,b=j;a<=n;a+=k,b^=1)
                vis[a][b]=1,tot++;
            End[tot]=true;
        }
    f[1][0][0]=1;
    for(int i=1;i<=tot;i++)
        for(int j=0;j<=n;j++){
            f[i+1][j][0]=(f[i][j][0]+f[i][j][1])%mod;
            if(!End[i])
                f[i+1][j+1][1]=f[i][j][0];
        }
    for(int i=0;i<=n;i++)
        g[i]=(f[tot][i][0]+f[tot][i][1])%mod;
    fac[0]=1;
    for(int i=1;i<=n;i++)fac[i]=1LL*i*fac[i-1]%mod;
    int ans=fac[n];
    for(int i=1,f=-1;i<=n;i++,f=-f){
        ans+=1LL*f*g[i]*fac[n-i]%mod;
        ans=(1LL*ans+mod)%mod;
    }
    printf("%d",ans);
}