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.chomp.split(" ").map(&:to_i)
s = gets.chomp.split("").map(&:to_i)
nums = []
now = 1
cnt = 0
n.times do |i|
  if s[i] == now
    cnt += 1
  else
    nums << cnt
    now = 1 - now
    cnt = 1
  end
end
if cnt != 0
  nums << cnt
end
if nums.size.even?
  nums << 0
end

sums = Array.new(nums.size + 1, 0)
nums.size.times do |i|
  sums[i+1] = sums[i] + nums[i]
end

add = 2 * k + 1

ans = 0

(0..(nums.size)).step(2) do |i|
  left = i
  right = [i + add, nums.size].min
  tmp = sums[right] - sums[left]
  if tmp > ans
    ans = tmp
  end
end
puts ans