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: Accepted)

from collections import deque
N,K=map(int,input().split())
S=input()
zeros=deque()
ichistart=0
zeros.append([-1,-1])
streak=0#0が何人連続した塊なのか
hajime=0
for k,i in enumerate(S):
    if i=="0":
        if streak==0:
            hajime=k
        streak+=1
    elif streak!=0:
        owari=hajime+streak-1
        streak=0
        zeros.append([hajime,owari])
if streak!=0:
    zeros.append([hajime,N-1])
zeros.append([N,N])
curmax=0
done=0
z=len(zeros)
if z<=K+1:
    print(N)
    done=1
if not done:
    for n,[s,f] in enumerate(zeros):
        if n+K+1<z:
            curmax=max(curmax,zeros[n+K+1][0]-f-1)
    print(curmax)