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 (7.3.0) (judge verdict: Accepted)

n, k = map(int, input().split())
s = input()

l_01 = []
l_10 = []
if s[0] == '1':
    l_01.append(0)
for i in range(n-1):
    if s[i] == '0' and s[i+1] == '1':
        l_01.append(i+1)
    elif s[i] == '1' and s[i+1] == '0':
        l_10.append(i+1)
if s[-1] == '1':
    l_10.append(n)

cnt_0 = len(l_01) - 1
if s[0] == '0':
    cnt_0 += 1
if s[-1] == '0':
    cnt_0 += 1
cnt_1 = len(l_01)

if k >= cnt_0:
    print(n)
else:
    res = 0
    i = 0
    while i + k < cnt_1:
        res = max(res, l_10[i+k] - l_01[i])
        i += 1
    if s[0] == '0':
        res = max(res, l_10[k-1])
    if s[-1] == '0':
        res = max(res, n - l_01[-k])
    print(res)