In an attempt to escape the Mischievous Mess Makers' antics, Farmer John has abandoned his farm and is traveling to the other side of Bovinia. During the journey, he and his *k* cows have decided to stay at the luxurious Grand Moo-dapest Hotel. The hotel consists of *n* rooms located in a row, some of which are occupied.

Farmer John wants to book a set of *k* + 1 currently unoccupied rooms for him and his cows. He wants his cows to stay as safe as possible, so he wishes to minimize the maximum distance from his room to the room of his cow. The distance between rooms *i* and *j* is defined as |*j* - *i*|. Help Farmer John protect his cows by calculating this minimum possible distance.
The first line of the input contains two integers *n* and *k* (1 ≤ *k* &lt; *n* ≤ 100 000) — the number of rooms in the hotel and the number of cows travelling with Farmer John.

The second line contains a string of length *n* describing the rooms. The *i*-th character of the string will be '0' if the *i*-th room is free, and '1' if the *i*-th room is occupied. It is guaranteed that at least *k* + 1 characters of this string are '0', so there exists at least one possible choice of *k* + 1 rooms for Farmer John and his cows to stay in.
In the first sample, Farmer John can book room 3 for himself, and rooms 1 and 4 for his cows. The distance to the farthest cow is 2. Note that it is impossible to make this distance 1, as there is no block of three consecutive unoccupied rooms.

In the second sample, Farmer John can book room 1 for himself and room 3 for his single cow. The distance between him and his cow is 2.

In the third sample, Farmer John books all three available rooms, taking the middle room for himself so that both cows are next to him. His distance from the farthest cow is 1.
7 2
0100100
2
5 1
01010
2
3 2
000
1
10 1
1101111101
6
2 1
00
1
3 1
010
2
8 7
00000000
4
7 6
0000000
3
112 12
0110101000000010101110010111100101011010011110100111111100011101011111000111101101110100111011110001100110110010
10
9 8
000000000
4
9 3
010001000
2
5 3
00000
2
8 7
00000000
4
6 1
000011
1
100 40
0010010100000100011100010100110001101100110000110010000000001010000111100000100100100101010010001100
30
93 79
000000000000000000011000000000000000000000000000000000000000000000010000000000100000100000000
42
31 11
0000001011011100010000000110001
7
47 46
00000000000000000000000000000000000000000000000
23
100 96
0000000000000010000010000000000000000000000000000000000000000000000000000010000000000000000000000000
50
491 89
01111101111111100000111010110001010001110111000010101111101000100010010111011101110110111101101010111000111000011100011010010010111111000011011010100110001000011100111000001011100010001111101111101000111001100110010100101000001110010100100100100101001100010101001000010000111110011000000100000100101000100101000001001101011011100000110101111110101001001000100110010000010110101011000101011001001011001000110000011111001110101011000000110101000000100110001101111000101001001001100001001110101
73
308 17
01000000100000000000000001000001000010000000000000000001001110000001010001000110000000000000100101000000010000001000000000001100000110000000000000000001000000000000000100000001000010001000000001000000000000000100010000000000000000000000000000000000001000000000001001101100000000000010000000000000000000000000
9
8 4
00111000
5
18 2
010111110111011110
5
29 3
01110011111111111111110110110
17
# cows

inp = input()

slice = inp.split()
cows = int(slice[1])

pattern = input()
	
def maxRooms(pat):
	for i in range(len(pattern), 0, -1):
		sub = '0' * i
		if sub in pattern:
			ini = pattern.index(sub)
			return i, ini, ini + i
	
			
def locateCows(pat, ini, fin, cows, distance):
	ini -= 1
	fin += 1
	
	if ini > 0:
		if pat[ini] == '0':
			cows -= 1
			if cows == 0:
				return distance
		
	if fin < len(pat):
		if pat[fin] == '0':
			cows -= 1
			if cows == 0:
				return distance
		
	return locateCows(pat, ini, fin, cows, distance + 1)
			
together = 0
initial = 0
final = 0	
		
together, initial, final = maxRooms(pattern)
print(locateCows(pattern, initial, final - 1, cows + 1 - together, 1))