Problem:
Score : 600 points

Problem Statement

Given is an integer sequence of length N+1: A_0, A_1, A_2, \ldots, A_N. Is there a binary tree of depth N such that, for each d = 0, 1, \ldots, N, there are exactly A_d leaves at depth d? If such a tree exists, print the maximum possible number of vertices in such a tree; otherwise, print -1.

Notes

A binary tree is a rooted tree such that each vertex has at most two direct children.

A leaf in a binary tree is a vertex with zero children.

The depth of a vertex v in a binary tree is the distance from the tree's root to v. (The root has the depth of 0.)

The depth of a binary tree is the maximum depth of a vertex in the tree.

Constraints

0 \leq N \leq 10^5

0 \leq A_i \leq 10^{8} (0 \leq i \leq N)

A_N \geq 1

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_0 A_1 A_2 \cdots A_N

Output

Print the answer as an integer.

Sample Input 1

3
0 1 1 2

Sample Output 1

7

Below is the tree with the maximum possible number of vertices. It has seven vertices, so we should print 7.

Sample Input 2

4
0 0 1 0 2

Sample Output 2

10

Sample Input 3

2
0 3 1

Sample Output 3

-1

Sample Input 4

1
1 1

Sample Output 4

-1

Sample Input 5

10
0 0 1 1 2 3 5 8 13 21 34

Sample Output 5

264

Solution in C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Runtime.InteropServices.ComTypes;
using System.Security.Cryptography.X509Certificates;
using System.Numerics;

namespace Atcoder01
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = Oneint();
            int[] A = Arrayint();
            int num = 0;

            for (int i = 0; i < N + 1; i++)
            {
                num += A[i];
            }

            long sumbranch = 1;
            long nowbranch = 1;
            long minasbranch = 0;
            long ans = 1;

            if (A[0] != 0)
            {
                ans = -1;
            }
            else
            {
                for (int i = 1; i < N + 1; i++)
                {
                    //枝の数を調整
                    if (num > nowbranch)
                    {
                        nowbranch += sumbranch;
                        sumbranch = sumbranch * 2;
                        if (num < nowbranch)
                        {
                            sumbranch -= (nowbranch - num);
                            nowbranch = num;
                        }
                    }

                    if (sumbranch - minasbranch <= 0)
                    {
                        ans = -1;
                        break;
                    }
                    else
                    {
                        ans += sumbranch;
                    }


                    minasbranch = A[i];
                    sumbranch -= A[i];
                }
            }

            Console.WriteLine(ans);
        }

        static double Mathing(double a, double b,double num)
        {
            double xlog = Math.Log(num);
            double result = Math.Pow(a, 2+xlog) + b*num;
            return result;
        }

        static string Tasu(string a1, string b1)
        {
            int anum = a1.Length;
            int bnum = b1.Length;
            int[] a = Array(a1);
            int[] b = Array(b1);

            string tasustring = "";
            if (anum < bnum)
            {
                int[] tasuans = new int[bnum + 1];
                for (int i = 0; i < anum; i++)
                {
                    tasuans[i] = a[i] + b[i];
                }
                for (int i = anum; i < bnum; i++)
                {
                    tasuans[i] = b[i];
                }
                for (int i = 0; i < tasuans.Length; i++)
                {
                    if (tasuans[i] >= 10)
                    {
                        tasuans[i] -= 10;
                        tasuans[i + 1]++;
                    }
                }
                for (int i = 0; i < tasuans.Length - 1; i++)
                {
                    tasustring = tasuans[i].ToString() + tasustring;
                }
                if (tasuans[tasuans.Length - 1] != 0)
                {
                    tasustring = tasuans[tasuans.Length - 1].ToString() + tasustring;
                }
            }
            else
            {
                int[] tasuans = new int[anum + 1];
                for (int i = 0; i < bnum; i++)
                {
                    tasuans[i] = a[i] + b[i];
                }
                for (int i = bnum; i < anum; i++)
                {
                    tasuans[i] = a[i];
                }
                for (int i = 0; i < tasuans.Length; i++)
                {
                    if (tasuans[i] >= 10)
                    {
                        tasuans[i] -= 10;
                        tasuans[i + 1]++;
                    }
                }
                for (int i = 0; i < tasuans.Length - 1; i++)
                {
                    tasustring = tasuans[i].ToString() + tasustring;
                }
                if (tasuans[tasuans.Length - 1] != 0)
                {
                    tasustring = tasuans[tasuans.Length - 1].ToString() + tasustring;
                }
            }
            return tasustring;
        }

        static int[] Array(string A)
        {
            int[] a = new int[A.Length];
            string num;
            for (int i = 0; i < A.Length; i++)
            {
                num = A.Substring(i, 1);
                a[A.Length - i - 1] = int.Parse(num);
            }

            return a;
        }


        private static string[] Arraystring()
        {
            return Console.ReadLine().Split(' ');
        }

        private static string Onestring()
        {
            return Console.ReadLine();
        }

        private static int Oneint()
        {
            return int.Parse(Console.ReadLine());
        }

        private static int[] Arrayint()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }

        private static long Onelong()
        {
            return long.Parse(Console.ReadLine());
        }

        static long[] Arraylong()
        {
            String[] input_line = Console.ReadLine().Split(' ');
            long[] input_num = new long[input_line.Length];
            for (int i = 0; i < input_line.Length; i++)
            {
                input_num[i] = long.Parse(input_line[i]);
            }
            return input_num;
        }
    }
}