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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

 #ランレングス圧縮とは RLE(Run Length Encoding)とも言われます。
#連続したデータを、ひとつ分のデータと連続した長さで表現します。
def rle(s):
    tmp, count, ans = s[0], 1, []
    for i in range(1,len(s)):
        if tmp == s[i]:
            count += 1
        else:
            ans.append((tmp,count))
            tmp = s[i]
            count = 1
    ans.append((tmp,count))
    return ans

   # AAABBCCCCA ⇒ A3B2C4A1

# 初期入力
import sys
input = sys.stdin.readline
N,K = (int(x) for x in input().split())
S =input().strip()

#0と1が何回続くか
a =rle(S)
a_len =len(a)
count =[0]*a_len
ans =0

if K >= (a_len +1)//2:
    ans =N
else:
    for i in range(a_len):
        j =0
        count_0 =0
        while count_0 <K and i+j+1 <a_len and j <a_len:
            count[i] +=a[i+j][1]
            if a[j][0]=="0":
                if count_0 ==K-1 and a[i+j+1][0] =="1":
                    count[i] +=a[i+j+1][1]
                count_0 +=1
            j +=1
    ans =max(count)
print(ans)