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<bits/stdc++.h>
using namespace std;
int n,k,t,a[4010],vis[4010][2];
long long fac[4010],g[4010],ans,f[4010][4010][2],p=924844033;
int main() {
    //freopen("permutation.in","r",stdin);
    //freopen("permutation.out","w",stdout);
    cin>>n>>k;
    for(int i=1; i<=n; i++)
        for(int j=0; j<2; j++)
            if(!vis[i][j]) {
                int x=i,y=j,len=0;
                while(x<=n) {
                    vis[x][y]=1;
                    len++;
                    x+=k;
                    y^=1;
                }t+=len;
                a[t]=1;
            }
    f[1][0][0]=1;
    for(int i=1; i<=t; i++)
        for(int j=0; j<=n; j++) {
            f[i+1][j][0]=(f[i][j][0]+f[i][j][1])%p;
            if(!a[i]) f[i+1][j+1][1]=f[i][j][0];
        }
    for(int i=1; i<=n; i++) g[i]=(f[t][i][0]+f[t][i][1])%p;
    fac[0]=1;
    for(int i=1; i<=n; i++) fac[i]=fac[i-1]*i%p;
    ans=fac[n];
    for(int i=1,j=-1; i<=n; i++,j=-j) ans=(ans+p+j*g[i]*fac[n-i])%p;
    printf("%lld\n",ans);
    return 0;
}