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;
typedef long long ll ;
const int maxn = 2010, mod = 924844033 ;
int dp[maxn * 2][maxn][2] ;
int fac[maxn] ;
bool link[2 * maxn] ;
int main() {
    int n, k, cnt = 0 ;
    scanf("%d%d", &n, &k) ;
    fac[0] = 1 ;
    for (int i = 1; i <= n; i ++) fac[i] = 1ll * fac[i - 1] * i % mod ;
    for (int i = 1; i <= k; i ++)
        for (int t = 1; t <= 2; t ++)
            for (int j = i; j <= n; j += k) {
                cnt ++ ;
                if (j != i) link[cnt] = 1 ;
            }
    dp[0][0][0] = 1 ;
    for (int i = 0; i < n * 2; i ++)
        for (int j = 0; j <= n; j ++) {
            dp[i + 1][j][0] = (dp[i][j][0] + dp[i][j][1]) % mod ;
            if (link[i + 1]) dp[i + 1][j + 1][1] = dp[i][j][0] ;
        }
    ll ans = 0 ;
    for (int i = 0; i <= n; i ++) {
        ll tmp = 1ll * (dp[n * 2][i][0] + dp[n * 2][i][1]) % mod * fac[n - i] % mod ;
        if (i & 1) ans = (ans - tmp + mod) % mod ;
        else ans = (ans + tmp) % mod ;
    }
    printf("%lld\n", ans) ;
    return 0 ;
}