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 <iostream>
#include <algorithm>
using namespace std;
typedef long long LL;
const int MOD = 924844033;
const int N = 2002;
int n,k;
LL f[N+2][N+2][2];
LL g[(N+2)*2][N+2];
LL fac[N];
void init() {
    fac[0]=1;
    for(int i=1;i<N;i++) fac[i]=fac[i-1]*i%MOD;
    f[0][0][0]=1;
    for(int i=0;i<N;i++){
        for(int j=0;j<=i;j++){
            (f[i+1][j][0] += f[i][j][0]+f[i][j][1]) %= MOD;
            (f[i+1][j+1][1] += f[i][j][0]) %= MOD;
        }
    }
    // k, n/k
    g[0][0]=1;
    for(int i=0;i<2*k;i++){
        int len=(n/k-1) + ((i/2 < n%k)?1:0); 
        for(int j=0;j<=n;j++){
            for(int x=0;x<=len;x++){
                g[i+1][j+x] += g[i][j] * (f[len][x][0] + f[len][x][1]);
                g[i+1][j+x] %= MOD;
            }
        }
    }
    /*
    for(int i=1;i<=n;i++) {
        printf("%d: %d\n", i, g[2*k][i]);
    }
    */
}
int main() {
    cin>>n>>k;
    init();
    LL ans = 0;
    for(int x=0;x<=n;x++) {
        LL tmp = g[2*k][x] * fac[n-x] % MOD;
        ans += x % 2 == 0 ? tmp : -tmp;
        ans = (ans % MOD + MOD) % MOD;
    }
    cout << ans << endl;
}