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 (3.8.2) (judge verdict: Accepted)

n, k = map(int, input().split())
s = input()
l=list()
s = s.replace("10","1,0")
s = s.replace("01","0,1")

l = [len(i) for i in s.split(",")]
r = 0
ans = 0

if s[0] == "1":
    r = min(k, len(l) - 1)
else:
    r = min(k-1, len(l) - 1)

t = l[r]

for j in range(1, k+1):
    #print(r,j,t,l[r-j],l[r+j])
    if r-j >= 0:
        #print("r-j >= 0:")
        t += l[r-j]
    if r+j < len(l):
        #print("r+j < len(l):")
        t += l[r+j]
ans = t
for i in range(r+2, len(l) ,2):
    for j in range(1, 3):
        if i-j-k >= 0:
            #print("l[i-j-k]", i-j-k, l[i-j-k])
            t -= l[i-j-k]
        if i+j+k-2 < len(l):
            #print("l[i+k+j]", i+j+k-2, l[i+j+k-2])
            t += l[i+j+k-2]
    ans = max(ans, t)
print(ans)