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)

#coding: euc-jp
class Main
  def self.main
    n, k = read2
    s = read1
    consecutive = [0]
    csnum = 1
    count = 0
    status = s[0].to_i
    n.times do |i|
      if status == s[i].to_i then
        consecutive[-1] += 1
      else
        consecutive += [1]
        csnum += 1
        status = s[i].to_i
      end
    end

    pos1 = 0
    pos2 = k * 2 - (s[0].to_i == 0 ? 1 : 0)
    return n if csnum <= pos2
    pos1.upto(pos2) do |i|
      count += consecutive[i]
    end
    max = count

    if s[0] == 0 then
      count += consecutive[pos2 + 1] if csnum <= pos2 + 2
      count += consecutive[pos2 + 2] if csnum <= pos2 + 3
      count -= consecutive[pos1]
      pos2 += 2
      pos1 += 1
      max = count if max < count
    end

    status = 1

    (pos2).upto(csnum - 1) do |i|
      status = (status + 1) % 2
      count += consecutive[i]
      count -= consecutive[pos1]
      pos1 += 1
      max = count if status == 1 && max < count
    end
    count -= consecutive[pos1]
    max = count if max < count

    return max
  end

  def self.read1
    gets.chomp
  end

  def self.read2
    gets.chomp.split.map(&:to_i)
  end
end

puts Main.main