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)

# coding: utf-8
import sys
import itertools

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

# 0か1の連続している人数のリスト、累積和
streak = [0, 0]
N, K = lr()
S = sr() + '2'
cur = 1
for i in range(N):
    if S[i] != S[i+1]:
        streak.append(cur)
        cur = 1
    else:
        cur += 1

streak_cum = list(itertools.accumulate(streak))
streak_cum.extend([streak_cum[-1], streak_cum[-1]])
if S[0] == '0':
    start = 0
else:
    start = 1
answer = 0

limit = len(streak_cum) - 1
for i in range(start, len(streak_cum), 2):
    result = streak_cum[min(limit, i+2*K+1)] - streak_cum[i]
    if result > answer:
        answer = result

print(answer)
# 52