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 OCaml (4.02.3) (judge verdict: Accepted)

let calc s k =
  if k = 0 then
    Array.fold_left (fun (v, w) (_, x) -> if x = '1' then max v (w+1), w+1 else v, 1) (0, 0) s |> fst else
  let t = Array.make 101010 0 in
  let ans, _, _, _, _ =
    Array.fold_left (fun (ans, cur, cs, ti, p) (i, x) ->
      match p, x with
      | '1', '1' -> (max ans (cur+1), cur+1, cs+1, ti, '1')
      | '0', '0' -> (max ans (cur+1), cur+1, cs+1, ti, '0')
      | '0', '1' -> begin
        t.(ti) <- cs;
        (max ans (cur+1), cur+1, 1, ti+1, '1')
      end
      | _ (* 1, 0 *) -> begin
        if ti < k then
          (max ans (cur+1), cur+1, cs+1, ti, '0')
        else
          (max ans (cur+1-t.(ti-k)), cur+1-t.(ti-k), cs+1, ti, '0')
      end) (0,0,0,0,'1') s
  in
  ans
let () =
  Scanf.scanf "%d %d %s" @@ fun n k s ->
  let s = Array.init n (fun i -> i, s.[i]) in
  max (calc s k) (calc (Array.map (fun (i, x) -> i, (if x = '0' then '1' else '0')) s) (k-1))
  |> Printf.printf "%d\n"