Longest Even Contiguous Subsequence (Large)

There is a sequence $S$ of length $N$. Every element of $S$ is a positive integer.

You may delete an element at any position in $S$, at most $K$ times in total.

For example, suppose $S$ is given as follows.

Sequence S : 1 2 3 4 5 6 7 8

If you delete the 4th element, 4, then $S$ becomes the following.

Sequence S : 1 2 3 5 6 7 8 

After deleting at most $K$ elements from $S$, find the maximum length of a contiguous subsequence consisting only of even numbers.

The first line contains the length $N$ of the sequence $S$ and the maximum number of deletions $K$, separated by a space.

The second line contains the $N$ integers that make up the sequence $S$, separated by spaces.

Print the maximum length of a contiguous subsequence consisting only of even numbers after deleting at most $K$ elements from $S$.

• $1 \le N \le 1,000,000$
• $1 \le K \le 100,000$
• $1 \le$ element value $\le 10^6$