Problem:
Score : 400 points

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.

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.

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.

Solution in LuaJIT (2.0.4) (judge verdict: Accepted)

n, k = io.read("*n", "*n", "*l")
s = io.read()
pos = 1
poslist = {}
cnt = 0
p1, p2 = string.find(s, "1+", pos)
while(p1 ~= nil) do
  cnt = cnt + 1
  poslist[cnt] = {}
  poslist[cnt].fst, poslist[cnt].lst = p1, p2
  pos = p2 + 1
  p1, p2 = string.find(s, "1+", pos)
end

if(#poslist < k) then
  print(n)
else
  res = 0
  for i = 1, #poslist - k do
   res = math.max(res, poslist[i + k].lst - poslist[i].fst + 1)
  end
  res = math.max(res, poslist[k].lst)
  res = math.max(res, n - poslist[#poslist - k + 1].fst + 1)
  print(res)
end