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: Runtime Error)

import sys,re,copy
input = sys.stdin.readline

N,K=[int(x) for x in input().strip().split()]

f=1
cnt=0
S=[]
r=0
for s in input().strip():
    s=int(s)
    if s==f:
        cnt+=1
    else:
        r+=cnt
        S.append(r)
        cnt=1
        f=1-f
else:
    r+=cnt
    S.append(r)
if len(S)%2==0:
    S.append(r)

Max=0
i=0
if len(S)==1:
    Max=S[0]
else:
    while True:
        r=i+2*K
        cnt=S[min(r,len(S)-1)]-S[max(i-1,0)]
        if cnt > Max:
            Max = cnt
        i+=2

print(Max)