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)

data = gets.split(" ").map{|nn|nn.to_i}
k = data[1]

members = gets.chomp

blocks = []

members = members.chars

lastman = members[0]
coutinuemen = 1
for i in 1..(members.size-1) do
  if lastman == members[i]
    coutinuemen += 1
  else
    blocks << coutinuemen
    coutinuemen = 1
    lastman = members[i]
  end
end
blocks << coutinuemen
enough = 100000000
if blocks[0] == "1"
  enough = (blocks.size / 2.0).floor
else
  enough = (blocks.size / 2.0).ceil
end


if enough <= k
  puts members.size.to_s
else
  getrange = k + k + 1
  maxsize = blocks.size - getrange
  tmpmax = -1

  if members[0] == "1"
    i = 0
    while i <= maxsize
      result = 0
      getrange.times do|offset|
        result += blocks[offset + i]
      end
      if tmpmax < result
        tmpmax = result
      end

      i += 2
    end
    #お尻のテスト
    if members.last == "0"
      result = blocks.last(getrange-1).inject(:+)
      if tmpmax < result
        tmpmax = result
      end
    end
  else
    i = 1
    while i <= maxsize
      result = 0
      getrange.times do|offset|
        result += blocks[offset + i]
      end
      if tmpmax < result
        tmpmax = result
      end

      i += 2
    end
    if members[0] == "0"
    result = blocks.first(getrange-1).inject(:+)
    if tmpmax < result
      tmpmax = result
    end
    end
  end

  puts tmpmax.to_s
end