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)

#!/usr/bin/env ruby

(n, k) = gets.chomp.split(/ /).map(&:to_i)

s = gets.chomp.split(//).map(&:to_i)

if s.join() =~ /^1+$/
  puts s.inject(:+)
  exit
end

flag = s[0]
array = []
count = 0

s.each do |i|
  if flag == i
    count += 1
  else
    array << count
    flag = i
    count = 1
  end
end
array << count

if s[0] == 0
  array.unshift(0)
end
if s[-1] == 0
  array.push(0)
end
#p array
max = 0
val = 0

(0..(k * 2)).each do |i|
  val += array[i]
end

max = val
#puts "first:#{max}"


#(0..(array.size - (k * 2))).each do |j|
0.step((array.size - (k * 2) - 2), 2) do |j|
  val -= (array[j] + array[j + 1])
  val += (array[j + k * 2 + 1] + array[j + k * 2 + 2])
#  puts "val:#{val}, j:#{j}"
  max = val if max < val
end

puts max