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;

#define int long long

const int maxn = 4e3 + 10, mod = 924844033;
int n, k, fac[maxn], inv[maxn], dp[maxn][maxn], cnt[maxn], ans, zar[maxn];
vector <int> V;

void pre() {
	fac[0] = 1;
	for (int i = 1; i < maxn; i++)
		fac[i] = (fac[i - 1] * i) % mod;
	for (int i = 0; i < maxn; i++)
		dp[i][0] = 1, dp[i][1] = i;

	zar[0] = 1;
	for (int i = 1; i < maxn; i++)
		zar[i] = -zar[i - 1];
	cnt[0] = 1;
	return;
}

int32_t main() {
	pre();
	cin >> n >> k;
	int val = n;
	for (int i = 0; i < k; i++) {
		val--;
		V.push_back(val / k);
	}
	for (int i = 2; i < maxn; i++) {
		for (int j = 2; j <= i; j++) {
			dp[i][j] = (dp[i - 1][j] + dp[i - 2][j - 1]) % mod;
		}
	}
	for (auto x : V) {
		int val = 2;
		while (val--) {
			for (int i = n; i >= 0; i--) {
				for (int j = 1; j <= min(x, i); j++) {
					cnt[i] = (cnt[i] + (cnt[i - j] * dp[x][j]) % mod) % mod;
				}
			}
		}
	}
	for (int i = 0; i <= n; i++) 
		ans = (ans + ((cnt[i] * zar[i] * fac[n - i]) % mod) + mod) % mod;
	cout << ans;
	return 0;
}