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())

flag = '0'
ans = []
for i, s in enumerate(S):
    if s == '1':
        if flag == '0':
            tmp = [0]*2
            tmp[0] = i+1
            flag = '1s'
        if flag == '1s' and i == n-1:
            tmp[1] = i+1
            ans.append(tmp)
    else:
        if flag == '1s':
            tmp[1] = i
            ans.append(tmp)
            flag = '0'
if S[0] == '0':
    ans.insert(0, [1, 1])
if S[n-1] == '0':
    ans.append([n, n])
# print(ans)
anser = []
if k >= len(ans):
    print(n)
else:
    for i in range(len(ans)):
        if i+k > len(ans)-1:
            break
        else:
            anser.append(ans[i+k][1]-ans[i][0]+1)
    print(max(anser))