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D - Handstand

Score : $400$ points

Problem Statement

$N$ people are arranged in a row from left to right.

You are given a string $S$ of length $N$ consisting of 0 and 1, and a positive integer $K$.

The $i$-th person from the left is standing on feet if the $i$-th character of $S$ is 0, and standing on hands if that character is 1.

You will give the following direction at most $K$ times (possibly zero):

Direction: Choose integers $l$ and $r$ satisfying $1 \leq l \leq r \leq N$, and flip the $l$-th, $(l+1)$-th, $...$, and $r$-th persons. That is, for each $i = l, l+1, ..., r$, the $i$-th person from the left now stands on hands if he/she was standing on feet, and stands on feet if he/she was standing on hands.

Find the maximum possible number of consecutive people standing on hands after at most $K$ directions.

Constraints

• $N$ is an integer satisfying $1 \leq N \leq 10^5$.
• $K$ is an integer satisfying $1 \leq K \leq 10^5$.
• The length of the string $S$ is $N$.
• Each character of the string $S$ is 0 or 1.

Input

Input is given from Standard Input in the following format:

$N$ $K$

$S$

Output

Print the maximum possible number of consecutive people standing on hands after at most $K$ directions.

5 1
00010

4

We can have four consecutive people standing on hands, which is the maximum result, by giving the following direction:

• Give the direction with $l = 1, r = 3$, which flips the first, second and third persons from the left.

14 2
11101010110011

8

1 1
1

1

No directions are necessary.