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
zero_c = 0
one_c = 0
group = Array.new
(S + (S[-1] == '0' ? ['1'] : ['0'])).each.with_index do |ch, i|
  if ch == '0'
    zero_c += 1
    if one_c > 0
      group.push([:one, one_c])
      one_c = 0
    end
  else # ch == '1'
    one_c += 1
    if zero_c > 0
      group.push([:zero, zero_c])
      zero_c = 0
    end
  end
end
zero_c = group.count { |(t, _)| t == :zero }
if zero_c <= K
  puts S.size
  exit 0
end

sum_list = Array.new
group.unshift([:one, 0]) if group[0][0] == :zero
group.push([:one, 0]) if group[-1][0] == :zero
sum = group[0][1]
1.step(by: 2, to: group.size - 2) do |i|
  _, zero_c = group[i]
  _, one_c = group[i + 1]
  sum += zero_c + one_c
  sum_list.push([sum, one_c])
end

ans = 0
(0..(sum_list.size - K)).each do |i|
  sum1, one_c = i == 0 ? [0, 0] : sum_list[i - 1]
  sum2, _ = sum_list[i + K - 1]
  n = sum2 - sum1 + one_c
  ans = n if n > ans
end
puts ans