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.

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.

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.

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.

见题面 Input 部分

见题面 Output 部分