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.

Examples

Input

5 1
00010


Output

4


Input

14 2
11101010110011


Output

8


Input

1 1
1


Output

1
import math                                                                                            

n,k = raw_input().split()
s = list(raw_input())


cnt = 0

prev = ''
tmp = ''
ar = []
for i in s:
    if i == '0' and prev !=  1:
        tmp += '0'
        prev = 0
    elif i == '0' and prev == 1:
        prev = 0
        ar.append(tmp)
        tmp = '0'
    elif i == '1' and prev != 0:
        tmp += '1'
        prev = 1
    elif i == '1' and prev == 0:
        prev = 1
        ar.append(tmp)
        tmp = '1'

ar.append(tmp)
k = int(k)


j = 0
cnt = 0
total = 0
m = 0

for i in ar:
    total += len(i)
    if '0' in i:
        cnt += 1
        if cnt == k + 1:                           
            total -= len(ar[j-2*k]) 
            if j >= 2*k + 1:                       
                total -= len(ar[j-2*k-1])
            cnt = k
    m = max(m, total)
    j += 1

print m

