Problem:
Score: 200 points

Problem Statement

There are three positive integers A, B and C written on a blackboard. E869120 performs the following operation K times:

Choose one integer written on the blackboard and let the chosen integer be n. Replace the chosen integer with 2n.

What is the largest possible sum of the integers written on the blackboard after K operations?

Constraints

A, B and C are integers between 1 and 50 (inclusive).

K is an integer between 1 and 10 (inclusive).

Input

Input is given from Standard Input in the following format:

A B C
K

Output

Print the largest possible sum of the integers written on the blackboard after K operations by E869220.

Sample Input 1

5 3 11
1

Sample Output 1

30

In this sample, 5, 3, 11 are initially written on the blackboard, and E869120 can perform the operation once.

There are three choices:

Double 5: The integers written on the board after the operation are 10, 3, 11.

Double 3: The integers written on the board after the operation are 5, 6, 11.

Double 11: The integers written on the board after the operation are 5, 3, 22.

If he chooses 3., the sum of the integers written on the board afterwards is 5 + 3 + 22 = 30, which is the largest among 1. through 3.

Sample Input 2

3 3 4
2

Sample Output 2

22

E869120 can perform the operation twice. The sum of the integers eventually written on the blackboard is maximized as follows:

First, double 4. The integers written on the board are now 3, 3, 8.

Next, double 8. The integers written on the board are now 3, 3, 16.

Then, the sum of the integers eventually written on the blackboard is 3 + 3 + 16 = 22.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;

namespace AtCoder.ABC096.B
{
    class Program
    {
        static void Main ()
        {
            var sc = new Scanner();
            var nums = sc.ArrayInt(3);
            int k = sc.NextInt();
            Array.Sort(nums);
            nums[2] = nums[2] * (int)Math.Pow(2, k);
            Console.WriteLine(nums.Sum());
        }

    }

    class Scanner
    {
        string[] s;
        int i;

        char[] cs = new char[] { ' ' };

        public Scanner ()
        {
            s = new string[0];
            i = 0;
        }

        public string Next ()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine ();
            while (st == "") st = Console.ReadLine ();
            s = st.Split (cs, StringSplitOptions.RemoveEmptyEntries);
            if (s.Length == 0) return Next ();
            i = 0;
            return s[i++];
        }

        public int NextInt ()
        {
            return int.Parse (Next ());
        }
        public int[] ArrayInt (int N, int add = 0)
        {
            int[] Array = new int[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = NextInt () + add;
            }
            return Array;
        }

        public long NextLong ()
        {
            return long.Parse (Next ());
        }

        public long[] ArrayLong (int N, long add = 0)
        {
            long[] Array = new long[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = NextLong () + add;
            }
            return Array;
        }

        public double NextDouble ()
        {
            return double.Parse (Next ());
        }

        public double[] ArrayDouble (int N, double add = 0)
        {
            double[] Array = new double[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = NextDouble () + add;
            }
            return Array;
        }

        public decimal NextDecimal ()
        {
            return decimal.Parse (Next ());
        }

        public decimal[] ArrayDecimal (int N, decimal add = 0)
        {
            decimal[] Array = new decimal[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = NextDecimal ();
            }
            return Array;
        }
    }

    static class MathExtensions
    {
        public static long Factorial (int n)
        {
            long fact = n;
            for (int i = n - 1; i >= 1; i--)
            {
                fact *= i;
            }
            return fact;
        }

        static long Combination (int n, int r)
        {
            long molecule = 1;
            for (int i = 0; i < r; i++) molecule *= n - i;
            long denominator = 1;
            for (int i = 1; i <= r; i++) denominator *= i;
            return molecule / denominator;
        }
    }

    static class IEnumerableExtensions
    {
        public static long Nearest (this IEnumerable<long> self, long target)
        {
            var min = self.Min (val => Math.Abs (val - target));
            return self.First (val => Math.Abs (val - target) == min);
        }
    }
}