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.strip
class String
  def string_cnt(arr)
    out=Array.new
    cnt=0
    change=arr.index(self[0])
    for i in 0...self.size
      if arr[change]==self[i]
        cnt+=1
      else
        out << cnt
        cnt=1
        change=(change+1)%arr.size
      end
    end
    out << cnt
    return out.delete_if{|x|x==0}
  end
end
as=S.string_cnt(["0","1"])

if S[0]=="0"
  if as.size <= 2*K
    ans=as.inject(:+)
  else
    cnt=0
    i=0
    while true
      cnt=cnt < as[i,2*K].inject(:+) ? as[i,2*K].inject(:+) : cnt
      i+=1
      break if i+2*K-1==as.size
    end
    ans = cnt
  end
else
  if as.size <= 2*K+1
    ans=as.inject(:+)
  else
    cnt=0
    i=0
    while true
      cnt=cnt < as[i,2*K+1].inject(:+) ? as[i,2*K+1].inject(:+) : cnt
      i+=1
      break if i+2*K==as.size
    end
    ans = cnt
  end
end
puts ans