Hypnotic experiment#11402
Your new hypnosis experiment involved people. Now these 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 of length , consisting of zeros and ones, representing the current status of these people, and a number . If the -th character of is , then the -th person from the left is awake, if it is , he is in hypnosis.
You can perform a hypnotic action no more than times. In one turn, you choose the numbers and (1 \le l \le r \le n) and perform a hypnotic action that will only affect -th, ( + )-th, ..., -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.
The first line contains two integers and (1 \le n, k \le 10^5). The next line gives . Each character of the string is either or , the length of the string is .
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 times.
\begin{example}\exmark{4 11001}\exmark{4}\end{example}
\begin{example}\exmark{3 1111}\exmark{3}\end{example}
Example 1
Example 2
Let's consider the first test. By choosing l = 2, r = 3, you can hypnotize people in the interval [, ]. As a result, consecutive people will be in a state of hypnosis.
In the second test, there is no need to conduct any hypnosis.