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<algorithm>
#define fo(i,a,b) for(i=a;i<=b;i++)
using namespace std;
typedef long long ll;
const int maxn=2000+10,mo=924844033;
int f[maxn][maxn][4],g[maxn],h[maxn],fac[maxn];
int i,j,k,l,r,t,n,m,ans;
int main(){
    scanf("%d%d",&n,&k);
    fac[0]=1;
    fo(i,1,n) fac[i]=(ll)fac[i-1]*i%mo;
    f[1][0][0]=1;
    f[1][1][2]=1;
    fo(i,1,n-1)
        fo(j,0,i)
            fo(t,0,3)
                if (f[i][j][t]){
                    (f[i+1][j][(t>>1)]+=f[i][j][t])%=mo;
                    if (t%2==0) (f[i+1][j+1][(t>>1)]+=f[i][j][t])%=mo;
                    (f[i+1][j+1][(t>>1)+2]+=f[i][j][t])%=mo;
                }
    g[0]=1;
    fo(r,1,k){
        t=r;
        l=1;
        while (t+k<=n){
            l++;
            t+=k;
        }
        fo(i,0,n) h[i]=0;
        fo(i,0,n)
            fo(j,0,l)
                fo(t,0,1)
                    if (i+j<=n) (h[i+j]+=(ll)g[i]*f[l][j][t]%mo)%=mo;
        fo(i,0,n) g[i]=h[i];
    }
    fo(i,0,n){
        t=(ll)g[i]*fac[n-i]%mo;
        if (i%2) (ans-=t)%=mo;else (ans+=t)%=mo;
    }
    (ans+=mo)%=mo;
    printf("%d\n",ans);
}