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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

int main(){
    long long n;
    cin >> n;
    long long a[n+1];
    for(long long i=0;i<=n;i++) cin >> a[i];
    bool flag=true;
    if(n==0&&a[0]!=1){
        cout << -1 << endl;
        return 0;
    }
    if(n==0&&a[0]==1){
        cout << 1 << endl;
        return 0;
    }
    long long b[n+1],c[n+1];
    b[n]=a[n];
    for(long long i=n-1;i>=0;i--){
        b[i]=b[i+1]+a[i];
    }
    c[0]=1;
    for(long long i=1;i<=n;i++){
        if(c[i-1]<=b[i-1])c[i]=(c[i-1]-a[i-1])*2;
        else c[i]=1000000000000000000LL;
        if(c[i]<=0) flag=false;
    }
    long long ans=0;
    for(long long i=0;i<=n;i++){
        ans+=min(b[i],c[i]);
    }
    if(flag) cout << ans << endl;
    else cout << -1 << endl;
}