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 N = 2000 + 10;
const int P = 924844033;
int n, k, dp[N << 1][N][2], a[N << 1], num, fac[N];
int main() {
    scanf("%d%d", &n, &k);
    for (int i = fac[0] = 1; i <= n; i++) fac[i] = 1ll * fac[i - 1] * i % P;
    for (int i = 1; i <= k; i++) {
        for (int j = i; j <= n; j += k) a[++num] = j;
        for (int j = i; j <= n; j += k) a[++num] = j;
    }
    dp[1][0][0] = 1;
    for (int i = 2; i <= (n << 1); i++) {
        for (int j = 0; j <= (i / 2); j++) {
            dp[i][j][0] = (dp[i - 1][j][0] + dp[i - 1][j][1]) % P;
            if (j && a[i] - a[i - 1] == k) dp[i][j][1] = dp[i - 1][j - 1][0];
        }
    }
    int ans = 0;
    for (int i = 0; i <= n; i++) {
        int g = (dp[n << 1][i][0] + dp[n << 1][i][1]) % P;
        if (i & 1)
            ans = (ans - 1ll * fac[n - i] * g % P + P) % P;
        else
            ans = (ans + 1ll * fac[n - i] * g) % P;
    }
    printf("%d\n", ans);
    return 0;
}