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 (2.7.1) (judge verdict: Accepted)

N,K=gets.split.map(&:to_i)
S=gets.chomp.chars

arr = S.chunk {|c| c}.map{|a,b| [a,b.length]}.to_a

i = 0
j = K
sum = 0
ret = 0
while i < arr.length
    c,n = arr[i]
    if c == '1'
        sum += n
    elsif 0 < j
        j -= 1
        sum += n
    else
        sum -= arr[i-K*2][1]
        sum -= arr[i-K*2-1][1] if 0 <= i-K*2-1
        sum += n
    end
    # p [ret,sum,i,j]
    ret = sum if ret < sum
    i += 1
end

puts ret