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>
using namespace std;
#define int long long
const int N=2010,mod=924844033;
int n,k,g[N<<1],f[N<<1][N][2],cnt,fac[N],ans;

signed main(){
    scanf("%lld%lld",&n,&k);
    for(int i=1;i<=k;i++){
        for(int j=i;j<=n;j+=k)g[++cnt]=(j==i);
        for(int j=i;j<=n;j+=k)g[++cnt]=(j==i);
    }
    f[0][0][0]=fac[0]=1;
    for(int i=1;i<=n;i++)fac[i]=1LL*i*fac[i-1]%mod;
    for(int i=0;i<n*2;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(!g[i+1])f[i+1][j+1][1]=f[i][j][0];
        }
    for(int i=0;i<=n;i++){
        int tmp=1LL*(f[n<<1][i][0]+f[n<<1][i][1])*fac[n-i]%mod;
        ans=(mod+(ans+(i&1?-1:1)*tmp)%mod)%mod;
    }
    printf("%lld\n",ans);
}