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>
using namespace std;

const int P = 924844033;
int n, K, tot, ans, fact[2010], chk[4010], f[4010][4010][2];

int main() {
    scanf("%d %d", &n, &K);
    for (int i = fact[0] = 1; i <= n; i++) {
        fact[i] = 1LL * i * fact[i - 1] % P;
    }
    f[0][0][0] = 1;
    for (int i = 1; i <= K; i++) {
        for (int j = i; j <= n; j += K) chk[++tot] = (i == j);
        for (int j = i; j <= n; j += K) chk[++tot] = (i == j);
    }
    for (int i = 0; i < 2 * n; i++) {
        for (int j = 0; j <= i; j++) {
            f[i + 1][j][0] = (f[i][j][0] + f[i][j][1]) % P;
            if (!chk[i + 1]) f[i + 1][j + 1][1] = f[i][j][0];
        }
    }
    for (int i = 0; i <= n; i++) {
        int s = (f[2 * n][i][0] + f[2 * n][i][1]) % P;
        ans = (ans + 1LL * (i & 1 ? P - 1 : 1) * fact[n - i] % P * s) % P;
    }
    printf("%d\n", ans);
    return 0;
}