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

• $2 \leq N \leq 2000$
• $1 \leq K \leq N-1$

Input

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

$N$ $K$

Output

Print the answer modulo $924844033$.

3 1

2

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

4 1

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.

4 2

9

4 3

14

425 48

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