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<algorithm>
#include<cmath>
#define N 2005
#define mod 924844033
using namespace std;
inline int read()
{
    char c=getchar(); int num=0,f=1;
    while (c<'0'||c>'9') { if (c=='-') f=-1; c=getchar(); }
    while (c<='9'&&c>='0') { num=num*10+c-'0'; c=getchar(); }
    return num*f;
}
int n,k,jc[N],tot,f[N<<1][N][2],ans;
bool lk[N<<1];
int main()
{
    n=read(); k=read();
    jc[0]=1; for (int i=1;i<=n;i++) jc[i]=1ll*jc[i-1]*i%mod;
    for (int i=1;i<=k;i++)
    {
        tot++; for (int j=i+k;j<=n;j+=k) lk[++tot]=true; 
        tot++; for (int j=i+k;j<=n;j+=k) lk[++tot]=true; 
    }
    f[0][0][0]=1;
    for (int i=0;i<n<<1;i++)
     for (int j=0;j<=min(i,n);j++)
     {
         f[i+1][j][0]=(f[i][j][0]+f[i][j][1])%mod;
         if (lk[i+1]) f[i+1][j+1][1]=f[i][j][0];
     }
    for (int i=0;i<=n;i++)
    {
        int tmp=1ll*(f[2*n][i][0]+f[2*n][i][1])*jc[n-i]%mod;
        if (i&1) ans=(ans-tmp+mod)%mod;
         else ans=(ans+tmp)%mod;
    }
    printf("%d",ans);
    return 0;
}