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.chars

nums = [N] + S.zip(['a'] + S, [*0...S.size]).select{|a, b, _| a != b}.map{|_, _, i| i}.reverse

Nums = nums.zip(nums.drop(1) + [0]).map{|i, j| i - j}.reverse

top = Nums.take(2*K + 1).inject(0, :+)
STDERR.puts "top: #{top}"
tmp = [top] + Nums.drop(2*K + 1).zip(Nums).map{|i, j| top += i - j}

STDERR.puts "tmp: #{tmp}"
Sums = if S[0] == "0" then
           tmp.zip([*0...tmp.size]).select{|i, j| j.even? }.map{|i, _| i}
       else
           tmp.zip([*0...tmp.size]).select{|i, j| j.odd? }.map{|i, _| i}
       end

STDERR.puts "Sums: #{Sums}"

p (Sums + [Nums.max]).max