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>
#include <cstring>
#include <cstdlib>
#include <algorithm>
using namespace std;

typedef long long ll;

const int N=4009;
const int md=924844033;

int n,k;
bool vis[N][N];
int ed[N],tot;
int f[N][N][2];
int g[N],fac[N];

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])
            {
                int len=0;
                for(int x=i,y=j;x<=n;x+=k,y^=1)
                    vis[x][y]=1,++len;
                ed[tot+=len]=1;
            }
    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])%md;
            if(!ed[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])%md;
    
    fac[0]=1;
    for(int i=1;i<=n;i++)
        fac[i]=(ll)fac[i-1]*i%md;
    
    ll ans=fac[n];
    for(int i=1,j=-1;i<=n;i++,j=-j)
        ans=((ll)ans+md+(ll)j*fac[n-i]*g[i]%md)%md;
    printf("%lld\n",ans);
    return 0;
}