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)

str1 = gets.split
N,K = str1[0].to_i, str1[1].to_i

S = gets.chomp
p = []
p[0] = 0
x = 1

if S[0] == "0"
  p[1] = 0
  x = 2
end

for i in 1...N
  if S[i] != S[i-1]
    p[x] = i
    x += 1
  end
end

p[p.size] = N

if p.size % 2 == 1
  p[p.size] = N
end

if p.size/2 - 1 <= K
  puts N
  exit
end

answer = 0
i = 1 + 2*K
j = 0

while i < p.size do
  if answer < p[i] - p[j]
    answer = p[i] - p[j]
  end
  i += 2
  j += 2
end

puts answer