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: Accepted)

import scala.collection.mutable.ArrayBuffer

object Scanner {
  private val buf = new Array[Byte](1024); private var ptr = 0; private var len = 0
  @inline private def isPrintableChar(c: Int): Boolean = 33 <= c && c <= 126
  @inline private def hasNextByte(): Boolean =
    if (ptr >= len) { ptr = 0; len = System.in.read(buf); len > 0 } else { true }
  @inline private def hasNext(): Boolean = {
    while (hasNextByte() && !isPrintableChar(buf(ptr))) ptr += 1
    hasNextByte()
  }
  @inline private def readByte(): Byte =
    if (hasNextByte()) { val res = buf(ptr); ptr += 1; res } else { -1 }
  def next(): String = {
    if(!hasNext()) ???
    val sb = new StringBuilder; var b = readByte()
    while (isPrintableChar(b)) { sb.append(b.toChar); b = readByte() }
    sb.toString
  }
  def nextInt(): Int = {
    val n = nextLong()
    if (n < Int.MinValue || Int.MaxValue < n) ???
    n.toInt
  }
  def nextLong(): Long = {
    if(!hasNext()) ???
    var minus = false; var b = readByte()
    if (b == '-') { minus = true; b = readByte() }
    def go (b: Byte, n: Long = 0): Long =
      if ('0' <= b && b <= '9') { go(readByte(), n * 10 + b - '0') }
      else if (minus) { -n } else { n }
    go(b)
  }
  def nextDouble(): Double = next.toDouble
}

object Main extends App {
  val n = Scanner.nextInt
  val k = Scanner.nextInt
  val s = Scanner.next
  val sArray = s.toCharArray

  var turningPoints = new ArrayBuffer[Int]

  sArray.zipWithIndex.foreach(a=>{
    if (a._2 == 0) {
      turningPoints += a._2
    } else {
      if (a._1 != sArray(a._2-1)){
        turningPoints += a._2
      }
    }
  })

  val result = turningPoints.zipWithIndex.map(t=>{
    if (sArray(t._1) == '0') {
      if ((t._2+2*k)>=turningPoints.length){
        n-t._1
      } else {
        turningPoints(t._2+2*k)-t._1
      }
    } else{
      if ((t._2+2*k+1)>=turningPoints.length){
        n-t._1
      } else {
        turningPoints(t._2+2*k+1)-t._1
      }
    }
  }).max

  println(result)
}