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 = 2005, mo = 924844033;
int n, k, cnt, tmp, ans, fac[N << 1], f[N << 1][N][2];
bool term[N << 1];

int main () {
	cin >> n >> k;
	fac[0] = 1;
	for (int i = 1; i <= n; ++i) fac[i] = 1ll * fac[i - 1] * i % mo;
	for (int i = 1; i <= k; ++i) {
		for (int j = (i - 1) % k + 1; j <= n; j += k) ++cnt;
		term[cnt] = 1;
		for (int j = (i - 1) % k + 1; j <= n; j += k) ++cnt;
		term[cnt] = 1;
	}
	f[1][0][0] = 1;
	for (int i = 1; i <= cnt; ++i) {
		for (int j = 0; j <= n; ++j) {
			f[i + 1][j][0] += (f[i][j][0] + f[i][j][1]) % mo;
			if (!term[i]) f[i + 1][j + 1][1] += f[i][j][0];
			f[i + 1][j][0] %= mo;
			f[i + 1][j + 1][1] %= mo;
		}
	}
	for (int i = 0, j = 1; i <= n; ++i, j = -j) {
		tmp = 1ll * (f[cnt][i][0] + f[cnt][i][1]) * fac[n - i] % mo;
		ans = (1ll * ans + tmp * j + mo) % mo;
	}
	cout << ans << endl;
	return 0;
}