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: Wrong Answer)

n, k = gets.split.map(&:to_i)
s = gets.chomp.split("")
gr = []
jd = s[0]
cnt = i = max = 0
s.each do |c|
  if c == jd
    cnt += 1
  else
    jd = c
    gr[i] = cnt
    cnt = 1
    i += 1
  end
end
gr[i] = cnt

cnt = sta = en = 0
div = odd = 0
if s[0] == "1"
  div = 2 * k
  odd = 2 * k - 1
elsif s[0] == "0"
  div = 2 * k - 1
  odd = 2 * k
end

while 1
  if cnt % 2 == 0
    en = sta + div
  else
    en = sta + odd
  end
  if en > i
    en = i
  end
  cmp = gr[sta..en].inject(:+)
  max = cmp if max <= cmp
  if en == i
    break
  end
  sta += 1
end
puts max