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 = STDIN.gets.chomp.split(' ').map(&:to_i)                          
S = STDIN.gets.chomp.split("").map(&:to_i)

renzoku = Array.new(0)

if S[0] == 0 then
  renzoku.push(0) # 1から始まる配列にしたいので,0から始まった場合は
                  # 無理やり先頭に0をpushする
end

now = S[0]
count = 0
S.each { |c|
  if (c == now) then
    count += 1
  else
    now = 1 - now # 0, 1を反転させる
    renzoku.push(count)
    count = 1
  end
}

renzoku.push(count) # 最後は尻切れトンボになるので,push

if (now == 0) then
  renzoku.push(0) # 1で終わる配列にしたいので,0で終わった場合は
                  # 無理やり最後に0をpushする
end

ruisekiWa = Array.new(0)
ruisekiWa.push(0) # 累積和は0からスタート
sum = 0
renzoku.each { |v|
  sum += v
  ruisekiWa.push(sum)
}
  
haba = K * 2 + 1

result = Array.new(0)

left = 0 # 1のあるところからスタート
right = 0

while left < ruisekiWa.length do
  if left + haba < ruisekiWa.length then
    right = left + haba
  else
    right = ruisekiWa.length - 1
  end
  result.push(ruisekiWa[right] - ruisekiWa[left])
  left += 2
end

puts result.max