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: Accepted)

def handstand(s, k)
  ones = []
  zeros = []

  prev = s[0]
  count = 0
  s.each_char do |c|
    if prev == c
      count += 1
    else
      if prev == '1'
        ones << count
      else
        zeros << count
      end
      count = 1
    end
    prev = c
  end

  s[-1] == '1' ? ones << count : zeros << count

  if zeros.count <= k
    return s.size
  end

  ones.unshift(0) if s[0] == '0'

  max = 0
  sum = 0
  used_one = []
  used_zero = []

  sum += ones.first
  used_one << ones.shift


  k.times do
    sum += zeros.first
    sum += ones.first
    used_zero << zeros.shift
    used_one << ones.shift
  end
  max = sum

  until zeros.empty? || ones.empty?
    sum -= used_one.first
    sum -= used_zero.first
    sum += zeros.first
    sum += ones.first
    used_zero << zeros.shift
    used_one << ones.shift
    used_zero.shift
    used_one.shift
    max = [max, sum].max
  end

  unless zeros.empty?
    sum -= used_zero.first if !used_zero.empty?
    sum -= used_one.first if !used_one.empty? && s[0] == '1'
    sum += zeros.first
    max = [max, sum].max
  end

  max
end

n, k = gets.split.map(&:to_i)
s = gets.chomp
puts handstand(s, k)