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(&:to_i)
S = gets.chomp
s_split = []
point = 0
S.chars.each_with_index{|c,i|
  next if i == 0
  if S[i] != S[i-1]
    s_split << S[point..(i-1)]
    point = i
  end

  if i == (S.size-1) && point != i
    s_split << S[point..i]
    point = i
  end
}

if s_split.size <= 2*K
  puts S.length
else
  ans = 0
  head_one_flag = s_split[0].include?('1')
  s_split.each_with_index{|e,i|
    if s_split.size < i + 2*K 
      break
    else
      tmp_ans = 0
      s_split[i,2*K].each{|e2|
        tmp_ans += e2.size
      }
      tmp_ans += s_split[i + 2*K].size if s_split[i + 2*K] != nil && head_one_flag
      ans = tmp_ans if ans < tmp_ans
    end
  }
  puts ans
end