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.chomp.split(" ")
s = gets.chomp.split("")
flag = s[0]
range = 0
max_size = 0
mono = []
zero = []
if flag == "0"
mono.push(0)
end

for i in s
  if flag == i
    range += 1
  else
    mono.push(range)
    if flag == "0"
      zero.push(range)
    end
    flag = i
    range = 1
  end
end
if flag == "0"
mono.push(0)
end
mono.push(range)

####
if k.to_i >= zero.length
puts mono.inject(:+)
else

ppl_size= k.to_i*2 + 1
step_size = mono.length - ppl_size + 1
step_size.times do |i|
  selected = mono[(i)..(i+ppl_size-1)]
#  print(selected, " ", i, " ",i+ppl_size-1,"\n")
  tmp_size = selected.inject(:+)
  if max_size < tmp_size
    max_size = tmp_size
  end
end
puts max_size-1
end
####