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 Lua (5.3.2) (judge verdict: Accepted)

-- D
local N, Kmax, _, tmp = io.read("n", "n", "l", "l")
local S = {}
local ZZ = string.byte('0')
for i=1, N do
    S[i] = string.byte(tmp, i, i) - ZZ
end
local rlast = 1
local k = 0
local left = 1
local ans = 0
for right=1, N do
    if rlast == 1 and S[right] == 0 then
        k = k + 1
    end
    rlast = S[right]
    while k > Kmax do
        local llast = S[left]
        left = left + 1
        if llast == 0 and S[left] == 1 then
            k = k - 1
        end
    end
    assert(right >= left)
    local v = right - left + 1
    if ans < v then
        ans = v
    end
end
print(ans)