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 Python (3.4.3) (judge verdict: Wrong Answer)

from sys import stdin
from itertools import combinations
from functools import reduce
from operator import add

def consecutive_ranges(s, char):
    ranges = []
    i = 0
    while i < len(s):
        cur = s[i]
        if cur == char:
            start = i
            end = i
            while i < len(s) and s[i] == char:
                end = end + 1
                i = i + 1
            r = start, end 
            ranges.append(r)
        i = i + 1
    return ranges


def merge_range(r1, r2):
    s1, e1 = r1
    s2, e2 = r2
    return s1, e2


# n: sの長さ
# k: 正整数(指示を出せる回数)
# s: 長さnの文字の配列
def solve(n, k, s):
    # ゼロが連続している範囲
    ranges = consecutive_ranges(s, '0')

    # 何回指示を出すか
    num_ops = min(len(ranges), k)
    max_length = max([e - s for s, e in consecutive_ranges(s, '1')])
    for i in range(0, min(len(ranges) - num_ops + 1, len(ranges))):
        start, end = merge_range(ranges[i], ranges[i + num_ops - 1])
        s2 = s[:]
        s2[start:end] = ['1'] * (end - start)
        length = max([e - s for s, e in consecutive_ranges(s2, '1')])
        if length > max_length:
            max_length = length
    return max_length


def main():
    lines = stdin.readlines()
    n, k = lines[0].split(' ')
    s = list(lines[1].strip())
    ans = solve(n, int(k), s)
    print(ans)