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<cstring>
#include<algorithm>
using namespace std;
typedef long long ll;
const int mod=924844033;
const int N=4005;
int n,k;
bool vis[N][2];
bool ed[N];
int tot;
int d[N][N][2];
int f[N];
int fact[N];
int main()
{
    //freopen("captain.in","r",stdin);
    //freopen("captain.out","w",stdout);
    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++;
                tot+=len;
                ed[tot]=1;
            }
    ed[0]=1;
    d[0][0][0]=1;
    for(int i=0;i<2*n;i++)
        for(int j=0;j<=n;j++){
            d[i+1][j][0]=(d[i][j][0]+d[i][j][1])%mod;
            if(!ed[i])
                d[i+1][j+1][1]=d[i][j][0];
        }
    for(int i=0;i<=n;i++)
        f[i]=(d[2*n][i][0]+d[2*n][i][1])%mod;
    fact[0]=1;
    for(int i=1;i<=n;i++)
        fact[i]=1ll*fact[i-1]*i%mod;
    int ans=0;
    for(int i=0,j=1;i<=n;i++,j=-j)
        ans=((1ll*ans+1ll*j*fact[n-i]*f[i]%mod)%mod+mod)%mod;
    printf("%d\n",ans);
}