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 _ = 4e3 + 10;
const ll mod = 924844033;
int tot, N, K, edge[_];
ll f[_][_][2], fac[_], ans = 0;

int main() {
	scanf("%d%d", &N, &K);
	fac[0] = 1;
	for (int i = 1; i <= N; ++i) fac[i] = 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) {
				++tot;
				if (j != i) edge[tot] = 1;
			}
	f[0][0][0] = 1;
	for (int i = 1; i <= N * 2; ++i) {
		for (int j = 0; j <= i / 2; ++j) {
			f[i][j][0] = (f[i][j][0] + f[i - 1][j][0] + f[i - 1][j][1]) % mod;
			if (edge[i] && j > 0) f[i][j][1] = (f[i][j][1] + f[i - 1][j - 1][0]) % mod;
		}
	}
	ll p = 1;
	for (int i = 0; i <= N; ++i) {
		ans = (ans + p * (f[N * 2][i][0] + f[N * 2][i][1]) % mod * fac[N - i] % mod + mod) % mod;
		p *= -1;
	}
	printf("%lld\n", ans);
	return 0;
}