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)

_n, k = gets.chomp.split(' ').map(&:to_i)
s = gets.chomp

xss = []
s.split('').each do |x|
  if xss.empty?
    xss.push([x])
  else
    if xss.last[0] == x
      xss.last.push(x)
    else
      xss.push([x])
    end
  end
end

# p xss

def sum(xss)
  xss.map(&:size).reduce(0) { |acc, x| acc + x }
end

ans = 0
prev_sum = nil
prev_yss = nil
xss.each_with_index do |xs, i|
  next if i != 0 && xs[0] == '0'
  count = xs[0] == '0' ? 2 * k : 2 * k + 1
  yss = xss.slice(i, count)

  # p yss

  sum = nil
  if prev_sum
    prev_chunk = prev_yss[0][0] == '0' ? prev_yss.slice(0, 1) : prev_yss.slice(0, 2)
    current_chunk = yss[-1][0] == '0' ? yss.slice(-1, 1) : yss.slice(-2, 2)
    sum = prev_sum - sum(prev_chunk) + sum(current_chunk)
    # p "minus: #{prev_chunk}"
    # p "plus: #{current_chunk}"
    # p sum
  else
    sum = sum(yss)
    # p [sum]
  end
  # p yss
  ans = [ans, sum].max

  prev_sum = sum
  prev_yss = yss
  # p '-'
  break if i + count >= xss.size
end

puts ans