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)

import sys

def i2s():
    return sys.stdin.readline().rstrip()

def ii2ss(n):
    return [sys.stdin.readline() for _ in range(n)]

def sp2nn(sp, sep=' '):
    return [int(s) for s in sp.split(sep)]

def ss2nn(ss):
    return [int(s) for s in list(ss)]

def analyze(S):
    data = []
    s0 = S[0]
    sc = 0
    for i, s in enumerate(S):
        if s == s0:
            sc += 1
        else:
            data.append((s0, sc))
            s0 = s
            sc = 1
    data.append((s0, sc))
    return data

def main(ss):
    N, K = sp2nn(ss[0])
    S = ss[1]
    data = analyze(S)
    cmax = 0
    
    for i in range(len(data)):
        c = 0
        j0 = i
        if data[i][0] == '0':
            j0 = i+2
        else:
            j0 = i+3
        for j in range(i, min(len(data), j0+(K-1)*2)):
            c += data[j][1]
        if cmax < c:
            cmax = c
    
    print(cmax)

main(ii2ss(2))