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 (2.7.1) (judge verdict: Accepted)

n,k = gets.chomp.split(" ").map(&:to_i)
s = gets.chomp.split("")
l = 0
r = -1
max = 0
zero = 0
pre = ""
while zero < k && r < n-1
  r += 1
  if s[r] == "1"
    if pre == "0"
      zero += 1
      if zero >= k
        while r < n-1
          if s[r+1] == "1"
            r += 1
          else
            break
          end
        end
      end
    end
  end
  pre = s[r]
end
if zero < k
  puts n
  exit
end
max = r - l + 1
pre = s[0]
while r < n-1
  l += 1
  if s[l] == "1" && pre == "0"
    nextzero = false
    pre = s[r]
    while !nextzero && r < n-1
      r += 1
      if s[r] == "1"
        if pre == "0"
          nextzero = true
          while r < n-1
            if s[r+1] == "1"
              r += 1
            else
              break
            end
          end
        end
      end
      pre = s[r]
    end
  end
  pre = s[l]
  max = [max,r-l+1].max
end
puts max