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.split.map(&:to_i)
s = gets.chomp
d = []
prev = "1"
cnt = 0
s.each_char do |c|
  if prev != c
    d << cnt
    cnt = 1
    prev = c
  else
    cnt += 1
  end
end
d << cnt
#p d
ans = 0
if d.length/2 <= K
  p d.reduce(:+)
  exit
end
ans = d[0,K*2+1].reduce(:+)
t = ans
(d.length/2-K).times do |i|
  t = t - d[i*2] - d[i*2+1] + d[K*2+i*2+1]
  t += d[K*2+i*2+2] if K*2+i*2+2 < d.length
  ans = t if t > ans
  #p t
end
p ans