Problem:
Score : 900 points

Problem Statement

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.

Sample Input 1

3 1

Sample Output 1

2

2 permutations (1, 2, 3), (3, 2, 1) satisfy the condition.

Sample Input 2

4 1

Sample Output 2

5

5 permutations (1, 2, 3, 4), (1, 4, 3, 2), (3, 2, 1, 4), (3, 4, 1, 2), (4, 2, 3, 1) satisfy the condition.

Sample Input 3

4 2

Sample Output 3

9

Sample Input 4

4 3

Sample Output 4

14

Sample Input 5

425 48

Sample Output 5

756765083

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <cstdio>

typedef long long LL;
const int Mod = 924844033;
const int MN = 2005;

int N, K;
int A[MN * 2], M;
int f[2][2][MN];

int main() {
	scanf("%d%d", &N, &K);
	for (int i = 1; i <= K; ++i) {
		for (int j = i; j <= N; j += i) A[++M] = j != i;
		for (int j = i; j <= N; j += i) A[++M] = j != i;
	}
	int o = 0;
	f[0][0][0] = 1;
	for (int i = 1; i <= M; ++i) {
		o ^= 1;
		for (int j = 0; j <= N; ++j) {
			f[o][0][j] = f[o][1][j] = 0;
			f[o][0][j] = (f[o ^ 1][0][j] + f[o ^ 1][1][j]) % Mod;
			if (A[i] && j)
				f[o][1][j] = f[o ^ 1][0][j - 1];
		}
	}
//	for (int j = 0; j <= N; ++j) printf("%d, ", (f[o][0][j] + f[o][1][j]) % Mod);
	int Coef = 1, Ans = 0;
	for (int i = N; i >= 0; --i) {
		Ans = (Ans + (i & 1 ? -1ll : 1ll) * Coef * (f[o][0][i] + f[o][1][i])) % Mod;
		Coef = (LL)Coef * (N - i + 1) % Mod;
	}
	printf("%d\n", (Ans + Mod) % Mod);
	return 0;
}