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.split('').map(&:to_i)


spl = [0]
s.each_with_index{|si, i|
	next if i == 0
	if s[i - 1] != si
		spl.push(i)
	end
}
spl.push(s.length)
p spl

mx = 0
spl.each_with_index{|spli, i|
	if i == 0 && s[0] == 0
		j = i + k * 2
	else
		j = i + k * 2 + 1
	end
	j = spl.length - 1 if j >= spl.length

	puts "#{spli} to #{spl[j]}" if mx < spl[j] - spli
	mx = spl[j] - spli if mx < spl[j] - spli
}

puts mx