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)

N, K = gets.split.map(&:to_i)
S = gets.chomp.chars.take(N)
zero_list = []
zero_start = nil
S.each.with_index do |ch, i|
  if ch == '0'
    zero_start = i unless zero_start
    if i == S.size - 1
      zero_list.push([zero_start, i])
    end
  else
    if zero_start
      zero_list.push([zero_start, i - 1])
      zero_start = nil
    end
  end
end

if zero_list.empty?
  puts N
  exit
end
ans = 0
(0..(zero_list.size - 1)).each do |i|
  s = if i == 0
    0
  else
    zero_list[i - 1][1] + 1
  end
  e_i = [i + K, zero_list.size - 1].min
  e = if e_i > zero_list.size - 1
    N - 1
  else
    zero_list[i + K][0] - 1
  end
  count = (e - s) + 1
  ans = count if count > ans
end
puts ans