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)

#参考　https://atcoder.jp/contests/abc124/submissions/4948803
from itertools import accumulate

n, k = map(int,input().split())
p = list(input())
a = []
pre = '1'
cnt = 0
for i in range(0,n):
     if pre != p[i]:
          a.append(cnt)
          cnt = 1
          pre = p[i]
     else:
          cnt += 1
a.append(cnt)
if pre == '1':
     a.append(0)

w = 2*k+1

if w >= len(a):
     print(n)
else:
     acc = list(accumulate(a))
     ans = 0
     acc = [0] + acc
     for i in range(0,len(a)-w+1,2):
          ans = max(ans,acc[i+w]-acc[i])
     print(ans)