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)

# Your code here!

a = []
a = gets.split.map(&:to_i)
n = gets.chomp
x = n.chars
#p x

t=x[0]
#p t
cnt=[]
#p cnt
c=0
for i in 0..a[0]-1
#p cnt
    if t == x[i]
        c+=1
    else
        t = x[i]
        cnt.push(c)
        c=1
        end
end
cnt.push(c)#次のループでpushされるので最後の分
#p cnt
#cnt.delete_at(0)
#p cnt

cnt_l = 1
if x[0]=="1"
    for i in 0..cnt.length-2*a[1]-1
    u = 0
        for j in i..i+2*a[1]
        u += cnt[j]
        end
    
    #p u
    if u >= cnt_l
        cnt_l = u
    end
    #p u
    end
else
     for i in 0..cnt.length-2*a[1]-1
    u = 0
        for j in i..i+2*a[1]
        u += cnt[j]
        end
    
    #p u
    if u >= cnt_l
        cnt_l = u
    end
    #p u
    end
end

puts cnt_l