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 <cstdio>
#include <algorithm>

using namespace std;

const int maxn = 2e3 + 10;
const int Mod = 924844033;

int f[2][maxn], g[2][maxn];
int fac[maxn];

int main()
{
	int n, k;
	scanf("%d%d", &n, &k);
	fac[0] = 1;
	for (int i = 1; i <= n; ++ i)
		fac[i] = 1ll * fac[i - 1] * i % Mod;
	g[0][0] = 1;
	int cur = 0, lst = 1;
	for (int T = 2; T; -- T)
	{
		for (int i = 1; i <= k; ++ i)
		{
			int t = (n - i + k) / k - 1;
			if (!t) continue;
			swap(cur, lst);
			for (int j = 1; j <= n; ++ j)
				f[cur][j] = (f[lst][j - 1] + g[lst][j - 1]) % Mod;
			for (int j = 0; j < n; ++ j)
				g[cur][j] = (f[lst][j] + g[lst][j]) % Mod;
			while (-- t)
			{
				swap(cur, lst);
				for (int j = 1; j <= n; ++ j)
					f[cur][j] = g[lst][j - 1];
				for (int j = 0; j < n; ++ j)
				
					g[cur][j] = (f[lst][j] + g[lst][j]) % Mod;
			}
		}
	}
	int ans = 0;
	for (int i = 0; i <= n; ++ i)
		(ans += (long long) (i & 1 ? -1 : 1) * (f[cur][i] + g[cur][i]) * fac[n - i] % Mod) %= Mod;
	printf("%d\n", (ans + Mod) % Mod);
	return 0;
}