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 qualified Data.List as L

main :: IO ()
main = do
    [n, k] <- map read.words <$> getLine
    cs <- getLine
    print $ solve k cs

solve :: Int -> String -> Int
solve k cs = go 0 0 0 [] [] $ L.group cs
  where
    go !res !acc !num0 fs rs (l@('1':_):css)
        = go (max res acc') acc' num0 fs (l:rs) css
      where
        acc' = acc + length l
    go !res !acc !num0 fs rs (l@('0':_):css)
        | num0 + 1 <= k = go (max res acc') acc' (num0 + 1) fs (l:rs) css
      where
        acc' = acc + length l
    go !res !acc !num0 [] rs (l@('0':_):css) = go res acc num0 (reverse rs) [] (l:css)
    go !res !acc !num0 (f@('0':_):fs) rs (l@('0':_):css)
        = go (max res acc') acc' num0 fs (l:rs) css
      where
        acc' = acc - length f + length l
    go !res !acc !num0 (f@('1':_):fs) rs (l@('0':_):css)
        = go res acc' num0 fs rs (l:css)
      where
        acc' = acc - length f
    go res _ _ _ _ [] = res