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: Runtime Error)

def dfs(k,index,s, target)
=begin
  puts "k : #{k}"
  puts "index : #{index}"
  puts "s : #{s}"
  puts "target : #{target}"
=end
  copy = Marshal.load(Marshal.dump(s))
  copy[target].gsub!(/0/, '1')

  if k == 1 || index.empty?
    return [copy]
  end

  ret = []

  index.each do |i|
    ret += dfs(k-1, index - [i], copy, i)
  end

  return ret

end

n,k = gets.chomp.split(" ").map(&:to_i)

s = gets.chomp
one = s.split("0").compact.reject(&:empty?)
zero = s.split("1").compact.reject(&:empty?)

if zero.empty?
  puts one.size
  exit
end

index = [*0...zero.size]

inverted = []

index.size.times do
  i = index.shift
  inverted += dfs(k,index,zero,i)
end

max = 0
inverted.each do |inv|
  max = [max,one.zip(inv).flatten.reject(&:nil?).join.split("0").max_by{|c| c.size}.size].max
end

puts max