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)

from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime,random
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())

N,K = inpl()
S = list(map(int,list(str(input()))))
ss = []

cnt = 0
flag1 = (S[0] == 1)
if S[0] == 0:
    ss.append(0)

for s in S:
    if flag1 and s == 0:
        ss.append(cnt)
        cnt = 1
        flag1 = False
    elif not flag1 and s==1:
        ss.append(cnt)
        cnt = 1
        flag1 = True
    else:
        cnt += 1

ss.append(cnt)

l = 0
r = 2*K
tmp = sum(ss[l:r+1])
ans = tmp
while True:
    l += 2
    r += 2
    if r >= len(ss):
        break
    tmp -= ss[l-2] + ss[l-1]
    tmp += ss[r-1] + ss[r]
    ans = max(ans,tmp)

print(ans)