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).

Input

The input is given from Standard Input in the following format:
N K

Output

Print the answer modulo 924844033.

Constraints

• 2 ≦ N ≦ 2000
• 1 ≦ K ≦ N-1

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

见题面 Input 部分

见题面 Output 部分