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)

##templete
n, k = gets.chomp.split(" ").map { |e|  e.to_i }
s = gets.chomp

nums = []
num = "1"
count = 0

for i in 0..n-1 do
  if s[i] == num
    count += 1
  else
    nums.push(count)
    num = ((num.to_i + 1) % 2).to_s  #文字の切り替え
    count = 1
  end
end

nums.push(count)

if nums.length % 2 == 0
  nums.push(0)
end

add = 2 * k + 1

left = 0
right = 0
tmp = 0 # [reft, right)のsum
ans = 0

0.step(nums.length-1, 2) do |i|

  nextleft = i
  nextright = [i + add, nums.length].min

  # 左端の移動
  while nextleft > left
    tmp -= nums[left]
    left += 1
  end

  # 右端の移動
  while nextright > right
    tmp += nums[right]
    right += 1
  end
  ans = ans > tmp ? ans : tmp
end

puts ans