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 MAXN 4005
typedef long long lint;

using namespace std;

int n, m, total;
lint f[MAXN][MAXN][2], ans;
lint fac[MAXN];
bool illegal[MAXN];
const int mod = 924844033;

void init() {
    fac[0] = 1;
    for (int i = 1; i <= n; ++i)
        fac[i] = fac[i - 1] * i % mod;
}

int main() {
    scanf("%d%d", &n, &m);
    init();
    for (int i = 1; i <= m; ++i)
        for (int j = 0; j <= 1; ++j)
            for (int k = i; k <= n; k += m) {
                ++total;
                if (k == i)
                    illegal[total] = true;
            }
    f[0][0][0] = 1;
    for (int i = 1; i <= total; ++i)
        for (int j = 0; j <= i; ++j) {
            f[i][j][0] = (f[i - 1][j][0] + f[i - 1][j][1]) % mod;
            if (!illegal[i])
                f[i][j][1] = f[i - 1][j - 1][0];
        }
    for (int i = 0; i <= n; ++i)
        if (i & 1)
            ans = (ans - fac[n - i] % mod * (f[total][i][0] + f[total][i][1]) % mod) % mod;
        else
            ans = (ans + fac[n - i] % mod * (f[total][i][0] + f[total][i][1]) % mod) % mod;
    printf("%lld\n", (ans + mod) % mod);
}