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)

nk = STDIN.gets().split(" ")
n = nk[0].to_i
k = nk[1].to_i
s = STDIN.gets().chomp

now_len = 0
pos = Array.new
s.each_char.with_index do |c, i|
  if c == "1"
    if now_len > 0
      pos.push [i - now_len, now_len]
    end
    now_len = 0
  else
    now_len += 1
  end
end

pos.sort! { |a, b| b[1] <=> a[1] }

if pos.length > 0
  for i in 0..k - 1
    for j in 0..pos[i][1] - 1
      s[pos[i][0] + j] = "1"
    end
  end
end

len = 0
now_len = 0

s.each_char do |c|
  if c == "0"
    if now_len > len
      len = now_len
    end
    now_len = 0
  else
    now_len += 1
  end
end

if now_len > len
  len = now_len
end

puts len