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

white_blocks = []
black_blocks = []

wc = 0
bc = 0

S.each_char do |s|
  if s == '0'
    bc += 1
    white_blocks << ['W', wc] if wc > 0
    wc = 0
  else
    wc += 1
    black_blocks << ['B', bc] if bc > 0
    bc = 0
  end
end

white_blocks << ['W', wc] if wc != 0
black_blocks << ['B', bc] if bc != 0

list = []

if S[0] == '0'
  list = black_blocks.zip(white_blocks).flatten
else
  list = white_blocks.zip(black_blocks).flatten
end

list = list.compact.each_slice(2).to_a

ls = list.size
head = 0
tail = 0

color, val = list[0]
cnt = val
k = color == 'B' ? 1 : 0
ans = cnt

while tail <= head
  ans = cnt if ans < cnt && k <= K

  if head == ls - 1
    c, v = list[tail]
    k -= 1 if c == 'B'
    cnt -= v
    tail += 1
  elsif head < ls - 1 && k <= K
    head += 1
    c, v = list[head]
    k += 1 if c == 'B'
    cnt += v
  elsif tail < ls - 1 && k > K
    c, v = list[tail]
    k -= 1 if c == 'B'
    cnt -= v
    tail += 1
  end
end

puts ans