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.chomp.split.map(&:to_i)
s = gets.chomp

asyuku_ary = []
count = 0
# now
# first
for i in 0..(n-1)
    if i == 0
        # first = s[i]
        asyuku_ary << [s[i],1]
        now = s[i]
    else
        if now == s[i]
            asyuku_ary[-1][-1] += 1
        else
            now = s[i]
            asyuku_ary << [s[i], 1]
        end
    end
end
ruisekiwa = []
asyuku_ary.each do |item|
    if ruisekiwa == []
        ruisekiwa << item[1].to_i
    else
        ruisekiwa << item[1].to_i + ruisekiwa[-1]
    end
end
# p asyuku_ary
# p ruisekiwa
flag = false
if s[0].to_i == 1
    if 2 * k >= asyuku_ary.length
        flag = true
    else
        max = ruisekiwa[2 * k]
        now = 2*k
        last = -1
    end
else
    if 2 * k - 1 >= asyuku_ary.length
        flag = true
    else
        max = ruisekiwa[2 * k - 1]
        now = 2*k-1
        last = -2
    end
end

# p asyuku_ary.length
# p ruisekiwa
# p now
# p ruisekiwa[now]
if flag
    puts n
else
    while true
        # p max
        if now + 2 >= asyuku_ary.length
            now = asyuku_ary.length - 1
            last += 2
            max = [max, ruisekiwa[now] - ruisekiwa[last]].max
        else
            now += 2
            last += 2
            max = [max, ruisekiwa[now] - ruisekiwa[last]].max
        end
        if now >= asyuku_ary.length - 1
            break
        end
    end
    puts max
end