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C - Folia /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 注釈

• 二分木とは、根付き木であって、それぞれの頂点の (直接の) 子の個数が 2 以下であるものを指す。
• 根付き木の葉とは、子の個数が 0 である頂点を指す。
• 根付き木の頂点 v の深さとは、根付き木の根から v までの距離を指す。(根の深さは 0 である。)
• 根付き木の深さとは、根付き木の頂点の深さの最大値を指す。

### 制約

• 0 \leq N \leq 10^5
• 0 \leq A_i \leq 10^{8} (0 \leq i \leq N)
• A_N \geq 1
• 入力はすべて整数である

### 入力

N
A_0 A_1 A_2 \cdots A_N


### 入力例 1

3
0 1 1 2


### 出力例 1

7


### 入力例 2

4
0 0 1 0 2


### 出力例 2

10


### 入力例 3

2
0 3 1


### 出力例 3

-1


### 入力例 4

1
1 1


### 出力例 4

-1


### 入力例 5

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


### 出力例 5

264


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