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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Data.List (group)
import Data.Bool (bool)
import qualified Data.Sequence as Q

main :: IO ()
main = do
  (n : k : _) <- map read . words <$> getLine :: IO [Int]
  s <- getLine :: IO String
  let
    s' = bool id (0 :) (head s == '0') . map length . group $ s
    (pr, sf) = splitAt (2 * k + 1) s'
    go (m, l, q) (l0 : l1 : ls) = let {(l1' Q.:< q') = Q.viewl q; (l0' Q.:< q'') = Q.viewl q'; l' = l - l1' - l0' + l0 + l1} in go (max m l', l', q'' Q.|> l0 Q.|> l1) ls
    go (m, l, q) (l0 : _) = let {(l1' Q.:< q') = Q.viewl q; (l0' Q.:< _) = Q.viewl q'; l' = m - l1' - l0' + l0} in max m l'
    go (m, _, _) _ = m
  print . go (sum pr, sum pr, Q.fromList pr) $ sf