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: Time Limit Exceeded)

n, k = gets.split(' ').map(&:to_i)
s = gets.chomp

data = []
s.each_char do |c|
  if c == '0'
    if data.empty? or data[-1] > 0
      data.push(-1)
    else
      data[-1] -= 1
    end
  else
    if data.empty? or data[-1] < 0
      data.push(1)
    else
      data[-1] += 1
    end
  end
end

i = data[0] < 0 ? 1 : 0
m = data.length/2 + i
if k >= m
  puts n
else
  data.map!(&:abs)
  result = (0..(m-k)).map{|j|
    l = k*2 + 1 - (j == 0 ? i : 0)
    j = j*2     - (j == 0 ? 0 : i)
    data[j,l].inject(:+)
  }.max
  puts result.to_s
end