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: Runtime Error)

n, k = map(int, input().split())
s = str(input())

count = 1
Nums_count = []
now = s[0]
start = 0
for i in range(1,n):
    if s[i] == str(now):
        count += 1
    else:
        Nums_count.append([start, count])
        now = s[i]
        start = i
        count = 1
    if i == n-1:
        Nums_count.append([start, count])
if len(s) == 1:
    Nums_count.append([0,1])

Nums_count_rui = [[-1, 0]]
for i in range(len(Nums_count)):
    Nums_count_rui.append([Nums_count[i][0],Nums_count[i][1]+Nums_count_rui[-1][1]])

# print(Nums_count_rui)
ans = 0
m = len(Nums_count_rui)

if s[0] == '0' and m <= 2*k:
    ans = n
elif s[0] == '1' and m <= 2*k+1:
    ans = n

for i in range(1,m+1):
    if s[Nums_count_rui[i][0]] == '0':
        if i+2*k-1 >= m:
            tot = Nums_count_rui[-1][1] - Nums_count_rui[i-1][1]
        else:
            tot = Nums_count_rui[i+2*k-1][1] - Nums_count_rui[i-1][1]
    else:
        if i+2*k >= m:
            tot = Nums_count_rui[-1][1] - Nums_count_rui[i-1][1]
        else:
            tot = Nums_count_rui[i+2*k][1] - Nums_count_rui[i-1][1]
    ans = max(tot, ans)
print(ans)