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>
#include <cstring>
using namespace std;
const int MOD = 924844033;
int a[4100],fac[4100],dp[4100][4100][2],n,k,cnt;
int main(){
    fac[0]=1;
    for(int i=1;i<=4000;i++)
        fac[i]=(1LL*fac[i-1]*i)%MOD;
    scanf("%d %d",&n,&k);
    for(int i=1;i<=k;i++){
        for(int j=0;j+i<=n;j+=k)
            a[++cnt]=j+i;
        for(int j=0;j+i<=n;j+=k)
            a[++cnt]=j+i;
    }
    // printf("cnt=%d\n",cnt);
    a[0]=0x3f3f3f3f;
    dp[0][0][0]=1;
    for(int i=1;i<=cnt;i++){
        dp[i][0][0]=1;
        for(int j=1;j<=i;j++){
            dp[i][j][0]=(dp[i-1][j][1]+dp[i-1][j][0])%MOD;
            if(a[i]-a[i-1]==k)
                dp[i][j][1]=dp[i-1][j-1][0];
        }
    }
    int ans=0,F;
    for(int i=0;i<=n;i++){
        F=(dp[cnt][i][0]+dp[cnt][i][1])%MOD;
        ans=(ans+1LL*((i&1)?-1:1)*F*fac[n-i])%MOD;
    }
    printf("%d\n",(ans%MOD+MOD)%MOD);
    return 0;
}