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
#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(1000000)

INF = 10 ** 18
MOD = 10 ** 9 + 7

N, K = map(int, raw_input().split())
S = raw_input()
ls = []
cc = '1'
num = 0
for c in S:
    if cc == c:
        num += 1
    else:
        ls += [num]
        num = 1
        cc = c
ls += [num]
if cc == '0':
    ls += [0]
S = 0
for i in range(min(len(ls), 2 * K + 1)):
    S += ls[i]
ans = S
for i in range(2 * K + 1, len(ls), 2):
    S += ls[i]
    S += ls[i + 1]
    S -= ls[i - (2 * K + 1)]
    S -= ls[i - (2 * K)]
    ans = max(ans, S)
print ans