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)

require 'pp'
n,k = gets.split.map &:to_i
s = gets.chomp
class Array
  def sum
    self.inject(&:+)
  end
end
# 1100
# 11111で終わる時ずれる
# 00000で始まる時ずれる
# 0011
# 00000で終わる時ずれる
# 11111で始まる時ずれる
p [
s.gsub(/^0+/){|a|?1 * a.size}.gsub(/1+$/){|a|?0 * a.size}.chars.map(&:to_i).chunk_while{|a,b|(a==0 && b==1).!}.to_a
.map(&:size).each_cons(k).map(&:sum).max,
s.gsub(/^1+/){|a|?0 * a.size}.gsub(/0+$/){|a|?1 * a.size}.chars.map(&:to_i).chunk_while{|a,b|(a==1 && b==0).!}.to_a
.map(&:size).each_cons(k).map(&:sum).max
].max