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 collections import deque, defaultdict as ddic
from itertools import combinations, permutations, product
import bisect
import heapq

rs = lambda: stdin.readline().strip()
ri = lambda: int(rs())
rsl = lambda: stdin.readline().split()
rim = lambda: map(int, rsl())
ril = lambda: list(rim())

n, k = rim()
s = list(rs())
zeros = []
temp = []
instreak = False
for i, char in enumerate(s):
    if char == '0':
        if not instreak:
            zeros.append(i)
            instreak = True
    else:
        instreak = False

# 1111111
if not zeros:
    print(len(s))
else:
    zeros = [-1] + zeros + [len(s)]
    maximum = 0
    for kk in range(1, k+1):
        index = 0
        left = zeros[index]
        for i in range(kk+1, len(zeros)):
            right = zeros[i]
            streak = right - 1 - left
            if streak > maximum:
                maximum = streak
            index += 1
            left = zeros[index]

    print(maximum)