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)

# encoding:utf-8
import copy
import numpy as np
import random
import bisect #bisect_left　これで二部探索の大小検索が行える
import math


N,K = map(int,input().split())
S = str(input())

now,cnt = 1,0
Nums = []
for i in range(N):
    if S[i] == str(now):
        cnt += 1
    else:
        Nums.append(cnt)
        cnt = 1
        now = 1 - now

if cnt!=0:
    Nums.append(cnt)

if len(Nums)%2==0:
    Nums.append(0)

#累積和
Sums = [0]
tmp = 0
for i in range(len(Nums)):
    tmp += Nums[i]
    Sums.append(tmp)
# print(Nums)
# print(Sums)
ans = 0
Add = 2*K+1
for i in range(len(Sums)):
    if i%2==0:
        left = i
        right = min(i+Add,len(Sums)-1)
        tmp = Sums[right]-Sums[left]
        ans = max(tmp,ans)
print(ans)