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 sys
from collections import deque
import copy
import math
def get_read_func(fileobject):
    if fileobject == None :
        return raw_input
    else:
        return fileobject.readline



def main():
    if len(sys.argv) > 1:
        f = open(sys.argv[1])
    else:
        f = None
    read_func = get_read_func(f);
    input_raw = read_func().strip().split()
    [N, K] = [int(input_raw[0]), int(input_raw[1])]
    input_raw = read_func().strip().split()
    S = input_raw[0]
    count_list = []
    s_list = []
    j = 0
    count = 1
    for i in range(1, N):
        if S[i] == S[i - 1]:
            count += 1
        else:
            count_list.append(count)
            s_list.append(S[i - 1])
            count = 1
    count_list.append(count)
    s_list.append(S[N - 1])
    n = len(count_list)
    count = 1
    sum_list = [0 for i in range(n + 1)]
    for i in range(1, n + 1):
        sum_list[i] = sum_list[i - 1] + count_list[i - 1]

    max_s = 0
    for i in range(1, n + 1):
        if s_list[i - 1] == "0":
            k = 2 * K
        else:
            k = 2 * K + 1
        max_s = max(sum_list[i] - sum_list[max(i - k , 0)], max_s)
    print max_s








if __name__ == '__main__':
    main()
