Problem:
Score: 200 points

Problem Statement

M-kun has the following three cards:

A red card with the integer A.

A green card with the integer B.

A blue card with the integer C.

He is a genius magician who can do the following operation at most K times:

Choose one of the three cards and multiply the written integer by 2.

His magic is successful if both of the following conditions are satisfied after the operations:

The integer on the green card is strictly greater than the integer on the red card.

The integer on the blue card is strictly greater than the integer on the green card.

Determine whether the magic can be successful.

Constraints

1 \leq A, B, C \leq 7

1 \leq K \leq 7

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B C
K

Output

If the magic can be successful, print Yes; otherwise, print No.

Sample Input 1

7 2 5
3

Sample Output 1

Yes

The magic will be successful if, for example, he does the following operations:

First, choose the blue card. The integers on the red, green, and blue cards are now 7, 2, and 10, respectively.

Second, choose the green card. The integers on the red, green, and blue cards are now 7, 4, and 10, respectively.

Third, choose the green card. The integers on the red, green, and blue cards are now 7, 8, and 10, respectively.

Sample Input 2

7 4 2
3

Sample Output 2

No

He has no way to succeed in the magic with at most three operations.

Solution in Scala (2.13.1) (judge verdict: Accepted)

import java.security.KeyStore.TrustedCertificateEntry
import java.util
import java.util.regex.Pattern
import java.util.{ArrayList, Collections, Comparator, List => JList}

import scala.collection.immutable.TreeMap
import scala.math._
import scala.collection.mutable
import scala.collection.mutable.{ArrayBuffer, ListBuffer}
import scala.util.{Failure, Success, Try}

object Main{
  val LS = "\n"
  def main(args: Array[String]): Unit = {
    if (sys.env.getOrElse("TEST", "")=="1"){
      println(test());
    }else{
      val input=io.Source.stdin.getLines().mkString(LS);
      println(solve(input).trim());
    }
  }

  def init (nRows: Int, nCols: Int, default: Int) = Array.tabulate(nRows,nCols)( (x,y) =>  default)

  def sortIgnoreCase1(list: JList[String]): JList[String] = {
    val r = new ArrayList[String](list)
    Collections.sort(r, new Comparator[String] {
      override def compare(o1: String, o2: String): Int = o1.compareToIgnoreCase(o2)
    })
    r
  }


  def solve(input: String): String = {
    val abc = input.split(LS).head.split(" ").map(_.toInt)
    val k = input.split(LS).tail.head.toInt

    def f(kc: Int, res: List[Array[Int]], abc: Array[Int]): List[Array[Int]] = {
      if (kc == k) return res
      f(kc + 1, Array(2 * abc(0), abc(1), abc(2)) +: res, Array(2 * abc(0), abc(1), abc(2))) ::: f(kc + 1, Array(abc(0), 2 * abc(1), abc(2)) +: res, Array(abc(0), 2 * abc(1), abc(2))) ::: f(kc + 1, Array(abc(0), abc(1), 2 * abc(2)) +: res, Array(abc(0), abc(1), 2 * abc(2)))
    }
    val r = f(0, List.empty[Array[Int]], abc).map { eachList =>
      eachList(1) > eachList(0) && eachList(2) > eachList(1)
    }.find(i => i)

    if (r.isDefined) "Yes" else "No"
  }



  def divideDigits(num: Long, base: Long = 10L): List[Long] = {
    def proc(num: Long, base: Long, flg: Boolean): List[Long] = {
      var flag = flg
      val quotient = num / base
      val remainder = if (num % base == 0) {
        flag = true
        base
      } else if (flag) {
        flag = false
        val temp = num % base - 1
        if (temp == 0) {
          flag = true
          base - 1
        } else temp
      } else {
        flag = flg
        num % base
      }
      quotient match {
        case 0 =>
          if (flag) {
            List.empty
          } else List(remainder)
        case _ => remainder :: proc(quotient, base, flag)
      }
    }

    proc(num, base, false).reverse//.filterNot(_ == 0)
  }


  def medianCalculator(seq: Seq[Long]): Long = {
    //In order if you are not sure that 'seq' is sorted
    val sortedSeq = seq.sortWith(_ < _)

    if (seq.size % 2 == 1) sortedSeq(sortedSeq.size / 2)
    else {
      val (up, down) = sortedSeq.splitAt(seq.size / 2)
      (up.last + down.head) / 2
    }
  }

  def factorize(x: Long): List[Long] = {
    def foo(x: Long, a: Long = 2, list: List[Long] = Nil): List[Long] = a*a > x match {
      case false if x % a == 0 => foo(x / a, a    , a :: list)
      case false               => foo(x    , a + 1, list)
      case true                => x :: list
    }
    foo(x)
  }

  def divisors(n: Int): Vector[Int] = {
    val halfList = (1 to sqrt(n).toInt).toVector.filter(n % _ == 0).map(_.toInt)
    val reversedList = if (sqrt(n).floor == sqrt(n)) halfList.reverse.tail.map(n/_) else halfList.reverse.map(n/_)
    halfList ++ reversedList
  }

  def gcd(m: Long, n: Long): Long = n match {
    case 0 => m
    case _ => gcd(n, m % n)
  }
  def lcm(a: Long, b: Long): Long = a * b / gcd(a, b)

  val tests=List(
    """7 2 5
      |3""".stripMargin -> """Yes
                                 |
                                         |
                                       |
                                   |""".stripMargin
    ,
    """7 4 2
      |3""".stripMargin -> """No
                                 |
                                           |
                                |""".stripMargin
//    ,
//    """2 1
//      |-1 1000000000""".stripMargin -> """1000000000
//                                             |""".stripMargin,
//    """10 10
//      |1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1""".stripMargin -> """999983200
//                                                                                                |""".stripMargin,
//    """4 3
//      |1 2 3 0
//      |""".stripMargin -> """6""",
//    """4 3
//      |1 2 0 0
//      |""".stripMargin -> """0"""
  )

  def test():String= {
    return tests.map{case (i,o)=>(i.trim(),o.trim())}
      .zipWithIndex.map{
      case ((input,outputExpect),i)=>{
        val output=solve(input).trim();
        s"test${i+1}:"+(if(output==outputExpect){
          "Passed"
        }else{
          s"Failed\nexpect:\n${outputExpect}\noutput:\n${output}"
        })
      }}
      .mkString("\n");
  }



}