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 <iostream>
using namespace std;
const int mod = 924844033;
int N, K, sub[2009][2009][3], val[2009][2009], dp[2009][2009], fact[2009];
int main() {
	cin >> N >> K;
	fact[0] = 1;
	for (int i = 1; i <= N; i++) fact[i] = 1LL * fact[i - 1] * i % mod;
	sub[0][0][0] = 1; val[0][0] = 1;
	sub[1][0][0] = 1; val[1][0] = 1;
	for (int i = 2; i <= N; i++) {
		for (int j = 0; j <= i; j++) {
			sub[i][j][0] = val[i - 1][j];
			if (j >= 1) sub[i][j][1] = (sub[i - 1][j - 1][0] + sub[i - 1][j - 1][1]) % mod;
			if (j >= 1) sub[i][j][2] = sub[i - 1][j - 2][0];
			val[i][j] = ((sub[i][j][0] + sub[i][j][1] * 2 % mod) % mod + sub[i][j][2]) % mod;
		}
	}
	dp[0][0] = 1;
	for (int i = 0; i < K; i++) {
		int num = N / K + (N % K > i ? 1 : 0);
		for (int j = 0; j <= N; j++) {
			for (int k = 0; k <= num && k <= j; k++) {
				dp[i + 1][j] = (dp[i + 1][j] + 1LL * dp[i][j - k] * val[num][k]) % mod;
			}
		}
	}
	int ret = 0;
	for (int i = 0; i <= N; i++) {
		if (i % 2 == 0) ret = (ret + 1LL * fact[N - i] * dp[K][i]) % mod;
		else ret = (ret - 1LL * fact[N - i] * dp[K][i] % mod + mod) % mod;
	}
	cout << ret << endl;
	return 0;
}