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 Scala (2.11.7) (judge verdict: Wrong Answer)

import scala.io.{StdIn => in}
import scala.collection.{mutable => mu}

object Main extends App {
  val Array(n,k) = in.readLine.split(" ").map(_.toInt)
  val s = in.readLine.toArray.map(_ - '0')
  val buf0 = mu.ArrayBuffer.empty[Int]
  val buf1 = mu.ArrayBuffer.empty[Int]
  var cnt0 = 0
  var cnt1 = 0
  for(i <- 0 until n) {
    if(s(i) == 0) cnt0 += 1
    else if(s(i) == 1 && cnt0 > 0) {
      buf0.append(cnt0)
      cnt0 = 0
    }
    if(s(i) == 1) cnt1 += 1
    else if(s(i) == 0 && cnt1 > 0) {
      buf1.append(cnt1)
      cnt1 = 0
    }
  }

  if(s.last == 0) buf0.append(cnt0) else buf1.append(cnt1)

  var res = 0
  for(i <- 0 to buf0.size - k) {
    res = res max (buf1.slice(i,i+k+1).sum + buf0.slice(i,i+k).sum)
    // debug(buf1.slice(i,i+k+1).sum, buf0.slice(i,i+k).sum)
  }
  val ans = res
  println(ans)

  def debug(any:Any*):Unit = {
    if(this.getClass.toString != "class Main$")
      println(any.mkString(" "))
  }
}