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 <algorithm>
#include <cstdio>
using namespace std;
const int mo = 924844033;
const int N = 4005;
int n, k, a[N], m, f[N][N][2], g[N], fac[N] = {1};
//f[i][j][0 / 1]:把链拼一块。前i个点，选了j个边，上个点有没有选，方案 
int main() {
	scanf("%d%d", &n, &k);
	for(int i = 1; i <= n; i ++) fac[i] = 1ll * fac[i - 1] * i % mo;
	for(int i = 1; i <= min(k, n - k); i ++) {
		for(int j = i; j <= n; j += k) a[++ m] = j;
		for(int j = i; j <= n; j += k) a[++ m] = j;
	}
	f[1][0][0] = 1;
	for(int i = 2; i <= m; i ++) {
		f[i][0][0] = 1;
		for(int j = 1; j <= i / 2; j ++) {
			f[i][j][0] = (f[i - 1][j][0] + f[i - 1][j][1]) % mo;
			if(a[i] - a[i - 1] == k) f[i][j][1] = f[i - 1][j - 1][0];
		}
	}
	int ans = 0;
	for(int i = 0; i <= n; i ++) {
		g[i] = (f[m][i][0] + f[m][i][1]) % mo * 1ll * fac[n - i] % mo;
		if(i & 1) (ans += mo - g[i]) %= mo;
		else (ans += g[i]) %= mo;
	}
	printf("%d\n", ans);
	return 0;
}