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)

{-# LANGUAGE BangPatterns #-}
import Control.Arrow
import Control.Monad.Fix
import Data.Foldable
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VM
import qualified Data.ByteString.Char8 as B
import System.IO.Unsafe
import Debug.Trace

solve :: Int -> Int -> B.ByteString -> Int
solve n k ss = maximum
  [ accums
    VU.! ((i + k') `min` (gn - 1))
    -    (if i - k' - 1 >= 0 then accums VU.! (i - k' - 1) else 0)
  | i <- [0 .. gn - 1]
  , let k' =
          if is0AtNthGroup i then ((k - 1) `div` 2) * 2 + 1 else (k `div` 2) * 2
  ]
 where
  bss = unsafePerformIO $ VU.freeze $ fst $ B.foldl'
    ( \(acc, i) ch ->
      (unsafePerformIO $ VM.write acc i (ch == '1') >> return acc, i + 1)
    )
    (unsafePerformIO $ VM.new n, 0)
    ss

  (_, irevstream, gn) = fix
    ( \f (bs, acc, g) -> if VU.length bs == 0
      then (bs, acc, g)
      else if not (VU.head bs)
        then
          let (zeros, other) = VU.span not bs
          in  f (other, VU.length zeros : acc, g + 1)
        else
          let (ones, other) = VU.span id bs
          in  f (other, VU.length ones : acc, g + 1)
    )
    (bss, [], 0)

  accums :: VU.Vector Int
  accums = unsafePerformIO $ VU.freeze $ (\(x, _, _) -> x) $ foldr'
    ( \k (acc, i, prev) ->
      let cur = prev + k
      in  cur
            `seq` ( unsafePerformIO $ (VM.write acc i cur >> return acc)
                  , i + 1
                  , cur
                  )
    )
    (unsafePerformIO $ VM.new gn, 0, 0)
    irevstream

  is0AtNthGroup n = if not (VU.head bss) then even n else odd n

main = do
  let readInt = fmap (second B.tail) . B.readInt

  nk <- V.unfoldrN 2 readInt <$> B.getLine

  ss <- B.getLine
  print $ solve (nk V.! 0) (nk V.! 1) ss