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)

n, k = gets.split(' ').map{|a|a.to_i}
s = gets.to_s.chomp

# que に "0が連続する数", "1が連続する数" を格納
list_01 = []
counter = ''
s.chars.each do | c |
  if counter == ''
    counter = c
    next
  end

  if counter[0] == c
    counter = counter + c
  else
    list_01 << {s: counter.size, f: counter[0].to_i}
    counter = c
  end
end
list_01 << {s: counter.size, f: counter[0].to_i} if counter.size > 0

# 累積和を算出
list_01.each_with_index do | e01, i |
  if i != 0
    list_01[i][:s] += list_01[i-1][:s]
  end
end
list_01.unshift({s: 0, f: nil})

max = 0
1.upto(list_01.size-1) do | ind |
  sum = 0
  if list_01[ind][:f] == 0
    st = ind
    st -= 1 if ind > 1
    en = ind+2*k
    en = list_01.size-1 if en > list_01.size-1
    sum = list_01[en][:s] - list_01[st-1][:s]
  else # == 1
    en = ind+2*k+1
    en = list_01.size-1 if en > list_01.size-1
    sum = list_01[en][:s] - list_01[ind-1][:s]
  end
  max = sum if sum > max
end
p max