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>
#define mod 924844033
using namespace std;
int n,k;
int dp[4005][2005][2];
int d[4005],cnt,ans,fac[2005];

int main(){
    scanf("%d %d",&n,&k);
    for(int i=1;i<=k;i++){
        for(int j=0;j<2;j++) d[cnt+1]=1,cnt+=(n-i)/k+1;
    }
    dp[0][0][0]=1;
    for(int i=1;i<=cnt;i++){
        for(int j=0;j<=n;j++){
            dp[i][j][0]=(dp[i-1][j][0]+dp[i-1][j][1])%mod;
            if(!d[i]&&j+1<=n) dp[i][j+1][1]=dp[i-1][j][0];
        }
    }
    fac[0]=1;for(int i=1;i<=n;i++) fac[i]=1ll*i*fac[i-1]%mod;
    for(int j=0,v;j<=n;j++){
        v=1ll*(dp[cnt][j][0]+dp[cnt][j][1])*fac[n-j]%mod;
        if(j&1) (ans+=mod-v)%=mod;else (ans+=v)%=mod;
    }
    printf("%d\n",ans);

    return 0;
}