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>

const int maxn = 2010, mod = 924844033;

int n, m, K, ans, fac[maxn];
bool f[maxn << 1];
int dp[maxn << 1][maxn][2];

int main() {
	scanf("%d%d", &n, &K);
	fac[0] = 1;
	for (int i = 1; i <= n; ++i) {
		fac[i] = 1ll * fac[i - 1] * i % mod;
	}
	for (int i = 1; i <= K; ++i) {
		f[++m] = 1;
		for (int x = i + K; x <= n; x += K) {
			++m;
		}
		f[++m] = 1;
		for (int x = i + K; x <= n; x += K) {
			++m;
		}
	}
	dp[0][0][0] = 1;
	for (int i = 1; i <= m; ++i) {
		if(f[i]) {
			for (int j = 0; j <= n; ++j) {
				dp[i][j][0] = (dp[i - 1][j][0] + dp[i - 1][j][1]) % mod;
				dp[i][j][1] = 0;
			}
		}
		else {
			for (int j = 1; j <= n; ++j) {
				dp[i][j][1] = dp[i - 1][j - 1][0];
			}
			for (int j = 0; j <= n; ++j) {
				dp[i][j][0] = (dp[i - 1][j][0] + dp[i - 1][j][1]) % mod;
			}
		}
	}
	for (int i = 0; i <= n; ++i) {
		int x = 1ll * fac[n - i] * (dp[m][i][0] + dp[m][i][1]) % mod;
		if(i & 1) {
			(ans += mod - x) %= mod;
		}
		else {
			(ans += x) %= mod;
		}
	}
	printf("%d\n", ans);
	return 0;
}