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

# 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** (**1** ≤ **l** ≤ **r** ≤ **n**) 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** (**1** ≤ **n**, **k** ≤ `10`

). The next line gives ^{5}**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.

5 1 10010

4

2 2 11

2