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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

/*
-------関数一覧--------
arr1dto2d(Array) 一次元配列を二次元配列にします
pf(N)因数分解した結果をオブジェクトで返します
gcd(a,b)最大公約数を返します
lcm(a,b)最小公倍数を返します
num(a,b)a-bを返します。ソート用です
isPrime(n)素数かどうか真偽値で返します
isNumber(n)数かどうか真偽値で返します
arrsum(arr)配列の合計値を返します
*/
var inf = Number.MAX_SAFE_INTEGER;
function Main(input){
	input = input.split("\n");
	var arr = input[0].split(" ").map(Number).sort(function(a,b){return a-b;});
	const n = input[1];
	for(var i=0;i<n;i++){
		arr[0] *= 2;
		arr.sort(function(a,b){return a-b;});
	}
	console.log(arrsum(arr));
}Main(require("fs").readFileSync("/dev/stdin", "utf8").trim());
function arr1dto2d (arr){
	for(var i=0;i<arr.length;i++){
		arr[i]=arr[i].split("");
		}
	return arr;
}
function isPrime(n){
    if(false===Number.isInteger(n)){
        return false;
    }
    if(n<=1){
        return false;
    }
    if(2===n){
        return true;
    }
    if(0===n%2){
        return false;
    }
    var square_root = Math.floor(Math.sqrt(n));
    for(var i=3; i<=square_root; i+=2){
        if(0===n%i){
            return false;
        }
    }
    return true;
}
function isNumber(val){
	const pat = /^([1-9]\d*|0)$/;
	return pat.test(val);
}
function arr1dto2d (arr){
	for(var i=0;i<arr.length;i++){
		arr[i]=arr[i].split("");
		}
	return arr;
}
function factorialize(num) {
  if (num === 0) { return 1; }
  return num * factorialize(num-1);
}
function arr1dto2d (arr){
	for(var i=0;i<arr.length;i++){
    arr[i]=arr[i].split(" ").map(Number);
    }
  return arr;
}
function rotate(array) {
  const ROW = array.length;
  const COL = array[0].length;
  const row = ROW-1;
  var a = new Array(COL);
  for (var c=0; c<COL; c++) {
    a[c] = new Array(ROW);
    for (var r=0; r<ROW; r++) {
      a[c][r] = array[row-r][c];
    }
  }
  return a;
}
function part_in(base,push,st){
	for(var i=st,p=0;p<push.length;i++,p++){
		base[i] = push[p];
	}
	return base;
}
function part_reverse(arr,s,g){
	var push = arr.slice(s-1,g);
  push.reverse();
	arr = part_in(arr,push,s-1);
	return arr;
}
function zeroPadding(num,length){
    return (num + '000000000000000000000000000000000').slice(0,length);
}
function arrsum(arr){
    var sum = 0;
    for (var i=0,len=arr.length; i<len; ++i) {
        sum += arr[i]-0;
    };
    return sum;
}
function pf(n) {
    var result = {};

    if (n === 1) {
        return {"1":1}
    }

    var init = 2;

    while (n !== 1) {
        var i = init;
        while (i < Number.MAX_SAFE_INTEGER) {
            if (n % i === 0) {
                n /= i;
                if (!(result[i] > 0)) {
                    result[i] = 0;
                }
                result[i]++;
                break;
            }
            i++;
        }
        init = i;
    }
    return result;
}
function gcd(a, b) {
    if (b === 0){
        return a
    }
    return gcd(b, a % b)
}
function lcm(a,b) {
    var g = (n, m) => m ? g(m, n % m) : n
    return a * b / g(a, b)
}
function num(a, b) {
  return a - b;
}
function nibu(a,searchValue){
	var index = -1;

//調べる左端を表す添字(index)
var left = 0;

//調べる右端を表す添字(index)
var right = a.length-1;

//左端と右端にデータがある間は処理を繰り返す
while(left <= right){

    //左右の真ん中を表す添字(index)
    middle =Math.floor((left +right)/2);

    //真ん中の値と探す値を比較する
    if(a[middle]==searchValue){
        //一致した場合、変数に入れて処理終了
        index = middle;
        break;
    }else if(a[middle]<searchValue){
        //探す値より小さい場合、左側にはもっと小さい値しかないので左端の値を真ん中の値の右に移動する
        left = middle +1;
    }else{
        //探す値より大きい場合、右側にはもっと大きい値しかないので右端の値を真ん中の値の左に移動する
        right = middle -1;
    }
}
if(index!=-1) return true;
else return false;
}