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)

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

sl = []
c = 1
if (s[0] == "1"):
    sl.append(0)
for i in range(n):
    if (i != 0):
        if (s[i] == s[i-1]):
            c += 1
        else:
            sl.append(c)
            c = 1
sl.append(c)

ruisekiwa = [0]
sums = []
ans = 0
w = 2*k+1

if (w > len(sl)):
    print(n)
    exit()
for i in range(len(sl)):
    ruisekiwa.append(ruisekiwa[i] + sl[i])
# print(sl)
# print(ruisekiwa)
for i in range(len(sl)):
    if(k % 2 == 1 and i % 2 == 0 or k % 2 == 0 and i % 2 == 1):
        left = i-k
        if (left < 0):
            left = 0
        right = i + k+1
        if (right >= len(ruisekiwa)):
            right = len(ruisekiwa)-1
        # print(ruisekiwa[right], "-", ruisekiwa[left],
        #      "=", ruisekiwa[right]-ruisekiwa[left])
        ans = max(ans, ruisekiwa[right]-ruisekiwa[left])
print(ans)