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)

def hanntenn(n):
    if n=="0":
        return "1"
    else:
        return "0"
from itertools import combinations

def numcheck(s):
    maxlen = 0
    j = 0
    for i in range(len(s)):
        if i >= len(s):
            return maxlen
        
        if s[i] == "1":
            j = i
            while(j+1 < len(s) and s[j+1] == "1"):
                j+=1
            _len = j-i+1
            if _len >= maxlen:
                maxlen = _len
            j+=1
        else:
            j+=1
            
    return maxlen

def zerocheck(s):
    pare = []
    j = 0
    for i in range(len(s)):
        i = j
        if i >= len(s):
            return pare
        
        if s[i] == "0":
            j = i
            while(j+1 < len(s) and s[j+1] == "0"):
                j+=1
            pare.append((i,j))
            j+=1
        else:
            j+=1
    return list(set(pare))
import copy
n,k = map(int, input().split())

s = input()
lists = list(s)

zerolists = zerocheck(s)
max_len = 0
print(zerolists)
for i in range(len(zerolists)):
    _lists = copy.copy(lists)
    for j in range(i,i+k):
        if j >= len(zerolists):
            continue
        for l in range(zerolists[j][0],zerolists[j][1]+1):
            _lists[l] = "1"
    _len = numcheck(_lists)
    if _len >= max_len:
        max_len = _len
if numcheck(lists) >= max_len:
    max_len = numcheck(lists)
print(max_len)