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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

//package javaapplication2;
 
import java.math.BigInteger;
import java.util.Scanner;
 
public class Main{
 
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
 
        int n = in.nextInt();
        BigInteger[] arr = new BigInteger[n + 7];
        BigInteger[] cnt = new BigInteger[n + 7];
        for (int i = 0; i <= n; i++) {
            arr[i] = in.nextBigInteger();
        }
        if (n == 0) {
            if (arr[0].equals(0)) {
                System.out.println("1");
            } else {
                System.out.println("-1");
            }
            System.exit(0);
        }
        for (int i = 0; i <= n; i++) {
            if (i == 0) {
                cnt[i] = BigInteger.ONE;
            } else {
                cnt[i] = (cnt[i - 1].subtract(arr[i - 1])).multiply(BigInteger.valueOf(2));
            }
            //System.out.println(cnt[i]);
            if (cnt[i].compareTo(BigInteger.ZERO) == -1) {
                System.out.println("-1");
                System.exit(0);
            }
        }
        if (cnt[n].compareTo(arr[n]) == -1) {
            System.out.println("-1");
            System.exit(0);
        }
        BigInteger ans = BigInteger.ZERO;
        for (int i = n; i >= 0; i--) {
            if (i == n) {
                cnt[i] = arr[i];
            } else {
                BigInteger temp = cnt[i + 1].add(arr[i]);
                if (temp.compareTo(cnt[i]) == -1) {
                    cnt[i] = temp;
                }
            }
            //System.out.println(cnt[i]);
            ans = ans.add(cnt[i]);
        }
        System.out.println(ans);
    }
 
}