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: Accepted)

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

tmp = []
current = s[0]
sum = 0
s.each do |c|
  if current == c
    sum += 1
  else
    tmp << {val: sum, type: current}
    sum = 1
    current = c
  end
end

tmp << {val: sum, type: current}

if tmp[0][:type] == "0"
  tmp.unshift({val: 0, type: "1"})
end

if tmp[-1][:type] == "0"
  tmp.push({val: 0, type: "1"})
end

take = k*2+1
total = tmp[0, take].reduce(0) {|a,e| a+=e[:val]}

ans = total

2.step(tmp.size, 2) do |i|
  next if tmp[i-1].nil?
  break if tmp[i+take-1].nil?
  total -= tmp[i-2][:val]
  total -= tmp[i-1][:val]
  total += tmp[i+take-2][:val]
  total += tmp[i+take-1][:val]
  ans = [ans, total].max
end

puts ans