Problem:
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.

Sample Input 1

5 1
00010

Sample Output 1

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.

Sample Input 2

14 2
11101010110011

Sample Output 2

8

Sample Input 3

1 1
1

Sample Output 3

1

No directions are necessary.

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

def count(s, n, k, pad)
    cnt = 0
    changeCnt = 0
    tmp = "1"
    n.times do |i|
        cnt += 1
        if s[i] != tmp
            if changeCnt == k && s[i] == '0'
                cnt -= 1
                break
            else
                if tmp == '1'
                    if pad != 0
                        pad -= 1
                        cnt = 0
                        changeCnt = 0
                        next
                    end
                    changeCnt += 1
                end
            end
            tmp = s[i]
        end
    end
    cnt
end

def test
    n, k = gets.split(" ").map(&:to_i)
    s = gets.chomp
    l = s.split("1").compact.reject(&:empty?).length
    ans = 0
    tmp = 0
    (l+1).times do |i|
        tmp = count(s.dup, n, k, i)
        ans = tmp if tmp > ans
    end
    ans
end

puts test