Competitions

# Hypnotic experiment

Your new hypnosis experiment involved n people. Now these n people are lined up from left to right, some of them are awake and some of them are in hypnosis.

You are given a string s of length n, consisting of zeros and ones, representing the current status of these people, and a number k. If the i-th character of s is 0, then the i-th person on the left is awake, if it is 1, he is in hypnosis.

You can perform a hypnotic action no more than k times. In one turn, you choose the numbers l and r (1lrn) and perform a hypnotic action that will only affect on l-th, (l + 1)-th, ..., r-th person. After a hypnotic action, only those who were awake before fall asleep, and those who were in a hypnotic state begin to wake up.

Find the size of the largest interval that can be achieved when everyone is in a hypnotic state.

#### Input data

The first line contains two integers n and k (1n, k105). The next line gives s. Each character of the string s is either 0 or 1, the length of the string is n.

#### Output

Print the size of the largest interval you can get when everyone is in a hypnotic state after applying the hypnosis action no more than k times.

#### Explanation

Let's consider the first test. By choosing l = 2, r = 3, you can hypnotize people in the interval [2, 3]. As a result, 4 consecutive people will be in a state of hypnosis.

In the second test, there is no need to conduct any hypnosis.

Time limit 1 second
Memory limit 128 MiB
Input example #1
5 1
10010

Output example #1
4

Input example #2
2 2
11

Output example #2
2

Source 2023 Azerbaijan, Semifinals, February 18, 10 - 11 classes