A - Even Odd subsequences

You are given an array $a$ of length $n$. A subsequence of this array is valid, if it satisfies these two conditions: - There shouldn't be any two even numbers within a distance of $K$, both which have been chosen in the subsequence. i.e. there shouldn't be two indices $i, j$ such that $a_i$ and $a_j$ are even, $|i - j| \leq K$ and $a_i$ and $a_j$ are in the subsequence. - Similarly, there should