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)

/*
    Arnab Chanda 
*/
 
// All imports here
 
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.InputStream;
import java.util.*;
import java.util.stream.Collectors;
 
// Template code starts here //
 
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Debugger debug = new Debugger(out);
        Objectify objectify = new Objectify(debug);
        Task solver = new Task();
        int test = 1;
        while(test-->0){
            solver.solve(1, in, out, debug, objectify);
        }
		out.close();
	}
}
 
class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;
 
    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }
 
    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }
 
    public int nextInt() {
        return Integer.parseInt(next());
    }
 
    public long nextLong() {
        return Long.parseLong(next());
    }
 
    public Double nextDouble() {
        return Double.parseDouble(next());
    }
 
    public float nextFloat() {
        return Float.parseFloat(next());
    }
 
}
 
class Debugger{
    PrintWriter out;
 
    Debugger(PrintWriter out){    
        this.out = out;
    }
 
    public <T> void printList(List<T> arrayList){
        for( Object ob: arrayList){
            out.print(ob+" ");
        }
        out.println();
    }
 
    public <T> void printSet(Set<T> set){
        for(Object ob: set){
            out.print(ob+" ");
        }
        out.println();
    }
 
    public <T> void printMap(Map<?,?> map){
        for(Object ob: map.keySet()){
            System.out.println(ob+" : "+map.get(ob));
        }
    }
}
 
class Objectify{
    
    Debugger debug;
 
    Objectify(Debugger ob){ debug = ob; }
 
    public void printArr(int[] arr){ debug.printList(Arrays.stream(arr).boxed().collect(Collectors.toList())); }
    public void printArr(double[] arr){ debug.printList(Arrays.stream(arr).boxed().collect(Collectors.toList())); }
    public void printArr(long[] arr){ debug.printList(Arrays.stream(arr).boxed().collect(Collectors.toList())); }
    public void printArr(char[] arr){ debug.printList( String.valueOf(arr).chars().mapToObj(c -> (char) c).collect(Collectors.toList())); }
    public void printArr(String[] arr){ debug.printList(Arrays.asList(arr)); }
 
    public void printMatrix(int[][] arr){ for(int a[]:arr) printArr(a); }
    public void printMatrix(double[][] arr){ for(double a[]:arr) printArr(a); }
    public void printMatrix(long[][] arr){ for(long a[]:arr) printArr(a); }
    public void printMatrix(char[][] arr){ for(char a[]:arr) printArr(a); }
    public void printMatrix(String[][] arr){ for(String a[]:arr) printArr(a); }
 
}
 
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 
// Template code ends here
 
 
class Task {
 
    final long MOD = (int)Math.pow(10,9)+7;
 
    public void solve(int testNumber, InputReader sc, PrintWriter out, Debugger debug, Objectify objectify) {
        
        // write your code here
        int n = sc.nextInt();
        int arr[] = new int[n+1];
 
        for(int  i = 0; i <= n; i++){
            arr[i] = sc.nextInt();
        }
 
        long[] max = new long[n+1];
        max[0] = 1;
 
        if(arr[0] == 1){
            out.println(-1);
            return;
        }
 
        for(int i = 1; i <= n; i++){
            max[i] = Math.max(max[i-1]*2 - arr[i-1]*2, Long.MAX_VALUE/4);
            if (max[i] < 0 || (arr[i] >= max[i] && i != n )){
                out.println(-1);
                return;
            }
        }
        // objectify.printArr(max);
        long ans = arr[n];
        long last = arr[n];
        for(int i = n-1; i >= 0; --i){
            last = Math.min(max[i], arr[i]+last);
            ans+=last;
        }
 
        out.println(ans);
 
    }
}