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

def go(s, k)
  a = s.chars.chunk(&:itself).map{|e, f| [e, f.size]}
  a = [['1', 0]] + a if a[0][0] == '0'
  a = a + [['1', 0]] if a[-1][0] == '0'
  k.times do
    break if a.size == 1
    j = 1.step(a.size - 2, 2).max_by{|i| a[i - 1][1] + a[i][1] + a[i + 1][1]}
    a[j - 1][1] = a[j - 1][1] + a[j][1] + a[j + 1][1]
    a.slice!(j, 2)
  end
  a.map{|x, y| x == '1' ? y : 0}.max
end

puts [go(S, K), go(S.gsub(/[01]/, '0' => '1', '1' => '0'), K - 1)].max