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: Accepted)

module Main where

import           Control.Monad
import           Data.List
import           Data.Ord
import           Data.List.Split
import           Data.Array.IO
import qualified Data.Vector.Unboxed as V

main :: IO ()
main = do
  [n, k] <- map read . words <$> getLine :: IO [Int]
  s <- getLine :: IO String
  let sums = (V.fromList . scanl (+) 0 . count . group) s
  print . V.maximum $ f sums k
  where
    count cs =
      let xs = if (head . head) cs == '0' then []:cs    else cs
          ys = if (even . length) xs then xs ++ [] else xs
      in  map length ys
    f sums k =
      let ls = V.length sums
          a  = 2 * k + 1
      in  V.fromList [(sums V.! min (i + a) (ls - 1)) - (sums V.! i) | i <- [0,2..(ls - 1)]]