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 MAXN	2005
#define P	924844033
template <typename T> void read(T &x) {
	x = 0; int f = 1;
	char c = getchar();
	for (; !isdigit(c); c = getchar()) if (c == '-') f = -f;
	for (; isdigit(c); c = getchar()) x = x * 10 + c - '0';
	x *= f;
}
long long dp[MAXN * 2][MAXN], fac[MAXN];
bool visited[MAXN * 2];
void update(long long &x, long long y) {
	x = (x + y) % P;
}
int main() {
	int n, k;
	read(n), read(k);
	int sum = 0;
	for (int i = 1; i <= k; i++) {
		int tmp = (n - i) / k;
		sum += tmp + 1;
		visited[sum] = true;
		sum += tmp + 1;
		visited[sum] = true;
	}
	for (int i = 0; i <= sum; i++)
		dp[i][0] = 1;
	for (int i = 2; i <= sum; i++)
	for (int j = 1; j <= n; j++) {
		if (!visited[i - 1]) update(dp[i][j], dp[i - 2][j - 1]);
		update(dp[i][j], dp[i - 1][j]);
	}
	fac[0] = 1;
	for (int i = 1; i <= n; i++)
		fac[i] = fac[i - 1] * i % P;
	long long ans = 0;
	for (int i = 0; i <= n; i++) {
		long long tmp;
		if (i & 1) tmp = P - 1;
		else tmp = 1;
		ans += tmp * fac[n - i] % P * dp[sum][i];
		ans %= P;
	}
	cout << ans << endl;
	return 0;
}