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



Sample input:
3
0 1 1 2


Sample output:
7

Submission status: Accepted

Solution code:
#N=int("22119")
#A=list(map(int, "0 1 1 1 0 3 1 1 0 1 1 2 12 6 1 5 1 1 0 1 3 0 7 2 13 3 2 4 3 9 0 3 0 3 0 1 5 0 2 3 0 2 0 1 8 11 0 0 0 14 2 0 2 7 8 3 1 0 0 5 2 7 0 1 1 6 0 6 17 0 4 12 4 3 8 3 0 3 0 0 4 7 1 1 1 1 1 0 3 0 3 0 3 1 1 1 0 0 3 1 9 8 11 8 18 3 0 0 3 1 14 3 1 7 17 9 0 3 1 0 3 0 0 7 0 2 3 0 1 4 0 2 2 11 9 12 9 3 1 1 17 0 0 5 1 2 14 2 1 5 0 1 1 5 5 5 5 7 2 0 14 3 0 1 4 3 1 1 0 1 2 4 5 2 0 11 9 1 1 1 0 3 0 1 2 5 0 10 1 0 7 3 1 9 11 6 39 9 68 153 1 1 15 5 1 1 1 0 0 2 4 15 0 2 1 3 2 3 8 3 1 1 1 1 0 2 2 1 4 1 2 6 2 0 2 2 19 0 0 0 14 3 1 0 3 1 0 0 5 2 2 3 7 6 8 15 19 65 33 14 54 3 15 69 6 1 62 119 131 251 528 311 503 144 144 16 76 2 4 6 4 4 52 2 7 9 0 0 7 0 2 1 1 7 2 2 7 0 19 0 3 0 1 0 10 3 1 0 2 3 1 0 0 7 0 0 2 6 5 8 2 9 13 7 20 1 4 2 2 3 0 0 1 7 13 0 0 2 4 14 1 5 0 0 5 4 1 0 3 14 4 4 3 2 12 3 3 5 5 8 6 6 49 103 16 4 42 9 1 2 10 2 13 1 18 8 0 11 0 11 82 93 28 67 19 9 31 21 0 0 7 1 1 1 0 1 0 1 9 15 9 3 12 34 47 17 35 25 9 0 3 1 1 1 0 1 4 2 3 0 2 2 3 0 1 2 1 3 21 1 1 1 1 1 0 0 1 11 3 4 0 5 2 6 3 1 0 2 0 2 4 2 16 8 24 6 13 3 8 4 20 24 52 0 44 5 4 2 1 2 6 0 6 0 7 1 1 0 0 2 9 4 2 1 2 0 2 6 30 11 5 16 56 43 20 6 8 4 7 1 1 0 1 0 10 3 0 3 1 0 1 0 4 0 18 12 18 4 45 4 0 1 7 12 1 3 0 3 1 8 24 7 3 146 29 99 11 33 21 34 11 1 5 23 4 2 3 0 0 0 10 10 3 1 0 3 0 2 1 2 4 0 9 1 17 13 8 0 5 2 4 4 0 12 3 7 5 1 1 1 0 2 0 7 0 0 1 4 8 22 1 0 4 4 20 2 10 1 3 5 0 3 0 0 2 4 0 21 12 3 11 37 0 0 39 47 21 4 9 92 17 2 3 7 3 4 0 0 0 6 17 59 6 30 0 7 0 3 0 2 0 3 8 3 1 1 1 1 0 3 0 2 3 0 1 1 6 4 5 1 6 3 6 6 2 2 2 1 3 4 1 0 9 4 0 6 1 1 7 2 5 4 0 2 6 11 1 1 1 0 0 6 1 5 0 2 1 2 1 2 9 21 8 17 3 0 3 10 8 9 7 6 14 0 7 1 1 0 2 0 0 0 4 13 41 40 83 8 45 7 5 9 12 8 7 0 2 1 5 0 1 1 6 5 1 7 2 3 1 0 25 12 14 9 3 0 6 0 12 21 1 6 2 10 1 4 3 1 1 0 1 4 3 1 1 0 1 1 8 1 2 0 1 19 18 1 9 9 1 0 2 3 1 0 1 2 7 0 3 0 1 2 4 2 2 11 10 2 3 33 32 1 3 3 1 4 2 8 3 18 44 7 1 1 1 1 1 0 2 2 0 3 2 9 6 1 24 7 1 7 15 8 2 17 3 4 0 0 8 15 0 1 2 7 0 1 2 4 2 5 2 16 3 0 29 13 48 24 20 7 1 1 1 0 0 5 5 1 1 1 1 1 0 1 4 2 0 1 1 8 8 42 12 10 39 3 1 1 28 9 57 10 7 34 22 7 7 27 16 0 4 37 0 6 9 0 9 5 1 0 1 3 0 10 3 0 1 5 0 2 0 2 3 0 23 1 8 76 7 3 7 22 30 9 41 19 10 7 0 3 1 1 1 1 1 0 3 0 3 0 2 2 1 2 1 3 17 9 0 0 1 10 2 7 3 0 20 2 8 33 8 4 0 29 2 6 3 0 0 1 3 21 0 1 2 6 3 0 2 1 3 5 0 2 2 2 1 4 0 5 3 4 1 4 3 0 3 1 0 2 3 1 0 0 2 8 0 8 11 4 5 9 1 3 16 25 5 0 3 1 0 0 7 0 0 0 15 0 0 3 9 1 1 0 2 3 0 1 3 0 4 13 0 1 20 3 1 0 2 1 0 8 0 1 19 2 32 3 8 5 54 13 3 2 4 1 0 6 36 6 15 0 3 2 47 22 11 20 7 6 1 5 4 20 4 18 11 0 1 5 1 0 1 3 2 7 0 1 3 3 0 3 10 4 22 2 3 0 1 2 3 9 0 0 4 3 5 4 4 2 3 8 23 76 73 17 0 22 38 20 57 224 102 654 43 194 847 289 671 272 108 259 410 56 113 261 28 109 70 81 35 44 19 1 0 3 1 0 2 0 7 0 0 4 3 1 9 9 3 9 13 3 8 154 94 3 10 5 16 11 1 1 1 0 3 1 0 3 0 2 1 2 5 0 5 1 5 23 4 33 51 0 27 9 78 112 2 106 197 537 55 30 8 5 1 12 30 26 5 43 74 72 129 36 156 221 148 30 5 9 7 2 2 9 0 4 4 1 9 13 73 47 60 40 86 2 0 3 1 4 14 26 0 4 3 2 1 17 21 3 1 13 16 3 1 23 47 31 20 117 61 0 2 3 1 1 0 2 3 1 1 0 0 0 10 0 21 5 1 1 0 0 3 9 1 1 1 0 0 1 6 1 8 27 18 6 18 66 2 2 2 3 1 1 1 0 2 0 1 1 20 11 1 1 1 0 2 2 3 1 1 0 0 0 13 5 0 0 1 6 0 20 23 0 2 3 0 2 0 6 2 1 4 1 0 8 7 0 3 0 1 3 1 8 0 6 2 2 3 0 0 1 9 8 1 0 11 0 2 2 2 0 5 0 8 6 2 3 1 0 2 2 0 0 7 2 17 24 9 1 5 9 1 1 0 0 5 3 4 1 1 8 2 1 2 6 3 1 0 1 2 5 2 3 0 2 11 34 4 48 6 2 33 5 1 1 1 0 1 5 1 1 1 0 3 1 1 1 1 0 2 2 0 1 7 7 11 3 5 0 3 0 3 1 0 2 2 0 4 0 7 5 7 12 2 6 101 93 65 8 308 25 178 23 26 76 1 0 8 20 18 16 48 7 2 7 30 33 0 6 16 31 26 8 52 4 29 35 214 8 19 10 83 20 11 0 1 5 1 1 0 0 5 2 2 6 2 7 23 4 0 7 0 1 0 5 7 6 9 9 9 0 3 1 0 1 1 1 17 1 0 3 1 1 0 0 1 11 3 2 3 9 1 0 1 4 0 4 7 1 0 2 3 1 1 1 0 2 1 2 6 2 0 4 3 0 11 11 2 4 14 48 7 0 3 0 0 7 1 1 0 1 5 1 0 3 1 1 0 2 2 1 4 2 0 5 3 5 1 0 0 4 2 1 10 19 3 7 12 3 1 1 0 2 1 5 1 1 1 0 2 1 2 6 0 2 4 8 8 4 15 5 13 16 11 7 4 2 51 6 20 38 0 70 53 77 150 8 20 22 3 0 2 3 1 0 1 1 2 7 8 1 21 26 3 6 29 5 8 28 3 77 22 1 9 5 0 3 10 21 39 28 1 5 0 1 2 1 11 5 0 1 2 4 3 0 9 10 12 20 2 5 6 12 0 10 3 3 8 18 43 6 23 0 2 2 0 6 1 4 3 0 2 3 0 3 0 3 0 1 5 0 0 2 3 10 3 25 0 2 0 4 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2 3 0 0 1 3 10 22 1 1 4 2 14 8 0 3 15 21 0 3 1 1 0 0 5 2 0 13 4 0 1 9 7 5 0 1 4 3 1 1 1 0 1 3 2 1 5 11 2 12 4 32 2 22 7 8 0 5 0 9 5 0 3 0 0 0 14 0 7 0 1 2 4 0 11 9 1 0 1 1 8 3 0 3 0 3 1 1 1 0 3 0 0 1 5 10 0 22 17 3 4 2 3 1 1 1 1 1 0 3 1 1 0 0 3 5 3 6 14 2 1 0 8 1 2 3 2 51 11 83 4 12 25 27 35 2 1 0 24 6 2 0 7 1 0 2 1 1 4 10 2 0 7 1 1 0 0 2 10 1 3 1 5 2 8 10 11 1 0 2 3 1 1 0 3 0 0 1 10 3 8 3 0 3 0 0 7 1 0 3 0 1 5 1 0 1 1 6 7 1 0 1 0 8 3 5 6 2 4 13 0 3 17 0 1 0 8 5 3 5 0 1 2 6 3 0 2 2 2 3 1 0 0 1 10 7 0 2 0 3 0 11 8 8 23 0 3 0 3 0 2 3 1 0 2 0 7 1 0 3 0 2 3 0 1 5 1 1 1 0 2 2 0 6 1 3 3 1 3 13 1 1 1 0 2 0 0 3 1 16 16 78 13 23 42 106 57 4 1 2 7 1 1 0 1 0 7 2 14 1 5 1 1 0 3 0 1 0 4 12 1 7 0 7 25 22 4 7 30 30 77 7 2 11 5 9 13 25 89 133 16 17 3 3 0 9 3 3 4 1 4 1 3 5 1 0 1 4 0 5 5 1 0 3 1 0 2 2 0 2 10 1 1 0 4 13 34 1 11 1 2 9 7 4 0 0 28 63 48 8 91 50 5 6 26 8 1 5 13 9 1 0 2 1 2 4 3 1 8 10 15 5 0 18 1 1 4 7 5 3 8 9 5 1 0 2 0 2 8 7 1 0 1 1 9 1 1 1 0 3 0 0 4 6 0 1 0 22 8 3 2 8 10 11 0 3 0 3 0 2 2 0 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3 3 23 17 20 3 3 25 1 13 3 3 17 4 1 2 14 24 0 99 22 4 7 0 3 1 1 0 3 1 1 1 0 1 0 9 0 8 1 8 3 5 16 6 17 3 12 38 19 15 4 1 0 6 6 1 6 22 7 10 20 7 22 22 1 1 8 3 1 0 2 2 1 1 6 3 8 0 2 6 11 1 0 1 2 1 1 14 0 45 3 3 5 0 1 3 5 1 1 1 1 0 3 0 3 0 2 1 4 3 1 1 1 0 3 0 0 5 1 3 9 4 7 3 0 19 12 8 0 0 22 9 11 0 10 27 54 47 5 8 25 2 32 5 11 7 28 1 0 6 9 2 2 1 16 1 19 0 10 1 5 1 0 2 2 0 1 9 2 0 16 16 4 15 27 65 35 31 131 6 38 33 107 43 100 56 41 76 18 23 11 23 8 3 17 0 0 3 0 0 28 19 4 10 2 2 2 1 1 0 16 1 0 25 1 7 1 7 1 4 11 1 0 3 1 1 0 0 1 8 5 13 0 3 0 0 7 1 1 1 1 1 0 3 1 0 0 6 3 0 0 6 0 5 2 3 5 0 14 0 14 14 2 15 8 1 0 0 11 7 16 35 7 20 0 3 9 0 2 3 1 0 2 0 4 4 3 9 1 1 1 0 2 1 0 2 17 5 0 2 3 0 3 1 0 3 0 3 0 0 0 5 14 13 1 4 7 3 1 10 3 18 39 68 9 9 15 11 22 243 25 0 2 1 1 7 0 9 4 1 5 0 1 2 6 2 0 2 6 1 13 7 9 25 1 0 3 0 3 0 2 0 5 4 0 7 0 0 0 1 7 16 57 0 9 2 5 3 2 0 8 15 0 2 3 1 1 0 1 5 1 1 1 1 1 1 1 0 0 4 1 3 14 13 0 6 4 6 4 18 15 14 13 15 2 1 3 80 7 1 6 21 0 11 1 0 0 0 14 2 2 1 5 1 1 0 3 0 2 0 2 11 1 1 1 0 3 1 1 1 1 1 0 2 2 1 2 7 0 3 0 3 1 0 0 7 0 1 4 0 0 8 15 0 3 1 0 2 2 2 2 1 1 1 17 1 1 1 1 1 1 0 1 2 3 2 15 1 1 1 1 1 1 0 3 1 0 2 3 1 0 1 4 2 1 0 0 16 4 23 1 1 0 2 3 0 3 1 1 1 0 3 0 0 5 0 3 7 14 7 5 8 9 19 9 24 36 156 101 13 368 216 176 2261 802 37 423 492 3642 172 90 4128 2337 222 1465 5491 333 7972 9562 1656 14228 1797 4 0 1 8 2 12 14 1 0 4 11 5 3 3 1 36 6 2 16 4 6 0 4 5 2 0 8 13 4 3 0 0 3 7 1 2 10 4 4 3 27 19 13 9 15 4 1 2 2 10 1 3 5 1 0 3 0 0 2 3 15 2 4 1 7 9 4 4 5 0 16 39 20 16 15 1 30 7 1 1 1 1 1 1 0 0 6 1 5 0 3 1 0 3 0 2 2 1 2 5 5 0 0 0 13 2 2 6 2 4 23 15 4 1 5 0 2 0 4 1 11 2 0 4 6 10 50 1 0 8 3 3 5 16 0 6 3 1 0 1 1 7 5 1 0 1 0 7 8 1 2 1 11 0 3 4 9 37 0 2 2 0 4 6 2 0 2 10 1 1 8 2 0 3 7 0 7 5 6 1 0 4 1 92 2 1 2 5 1 6 5 5 0 1 3 3 4 3 0 3 1 1 0 0 2 5 5 8 19 1 0 0 0 3 4 15 14 3 97 142 1 8 3 4 14 24 7 1 0 0 1 7 7 0 6 43 1 1 1 1 1 1 0 1 3 2 3 8 2 3 0 3 0 3 0 2 2 0 1 8 4 1 19 8 12 18 1 29 28 31 0 32 26 15 14 14 9 0 20 34 0 12 67 2 66 20 13 3 4 1 1 6 6 0 5 4 2 0 0 13 4 0 4 7 0 1 4 1 5 0 2 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13 4 3 0 3 0 2 0 6 3 1 1 0 2 2 0 4 3 3 12 2 3 0 1 0 2 10 4 23 15 0 0 23 1 1 1 0 1 4 2 1 0 4 7 8 4 9 13 16 11 124 13 178 1 30 21 19 3 2 2 8 0 15 0 0 3 7 4 3 0 2 1 0 11 1 0 2 3 0 3 0 3 0 1 3 5 1 1 0 2 1 4 1 4 3 0 1 4 3 1 0 0 7 1 1 0 2 2 3 1 1 1 1 1 0 3 1 1 0 2 1 2 4 7 0 0 2 9 2 7 1 0 0 5 1 0 8 23 0 2 2 0 2 0 22 1 5 0 1 5 1 0 3 0 1 5 1 1 1 0 3 1 1 1 0 0 2 1 17 9 1 0 2 3 1 0 0 5 1 0 8 14 18 3 1 1 0 1 0 6 7 8 1 2 1 0 22 11 1 1 1 1 0 0 4 3 2 5 16 11 0 3 0 3 1 0 3 1 0 1 4 3 0 0 3 0 4 16 28 4 3 8 0 5 2 4 2 8 1 9 7 0 1 14 12 0 14 1 1 6 6 3 1 1 0 1 4 1 0 5 11 0 8 0 7 17 1 0 3 1 1 1 0 2 1 4 0 7 1 0 0 2 9 3 4 0 4 0 11 2 8 8 13 2 1 12 0 2 3 14 3 1 14 4 7 1 0 3 0 3 1 1 1 0 2 3 1 0 3 1 1 0 0 3 5 3 10 5 5 1 1 1 0 0 4 6 2 2 2 1 2 0 4 12 13 21 0 1 2 6 1 0 5 10 4 5 0 9 5 1 0 0 5 4 1 0 0 6 0 26 16 17 104 315 21 3 37 5 4 36 13 3 2 2 3 14 4 3 2 4 17 10 1 3 0 31 7 16 35 6 13 3 37 0 0 7 1 1 0 1 0 0 2 21 1 54 20 102 2 2 3 0 3 1 0 3 1 0 0 2 9 2 6 1 5 0 1 0 4 2 15 4 35 9 17 0 3 0 0 5 4 3 0 2 3 1 0 1 5 0 0 0 7 14 6 1 2 3 1 12 10 3 0 0 1 10 3 3 10 4 3 7 3 5 0 1 1 8 3 1 1 1 0 0 4 0 13 0 3 0 4 50 7 35 13 1 0 0 6 1 2 7 0 3 1 0 3 1 0 1 5 1 0 2 3 0 3 0 3 0 1 4 3 1 0 0 1 13 1 1 1 0 2 0 0 2 9 35 3 5 1 0 3 0 3 0 1 2 7 1 1 0 2 1 3 3 0 8 5 5 1 0 3 0 3 1 1 0 3 1 1 1 1 1 0 3 0 3 0 1 1 9 1 0 2 1 2 0 4 22 3 0 2 3 0 0 3 2 9 1 6 10 12 1 153 37 68 2 5 7 23 15 41 25 5 48 10 3 15 17 30 12 9 2 37 28 8 17 12 0 5 2 3 8 0 3 8 3 0 3 1 1 1 1 0 1 1 1 5 22 2 3 0 1 28 42 38 15 51 83 115 44 48 90 751 1183 87 25 31 48 71 1 8 6 22 2 0 1 25 58 47 48 13 42 125 102 107 325 243 46 250 6 10 0 2 7 9 0 2 1 2 1 11 1 1 6 4 22 20 2 41 2 48 19 24 30 45 40 38 9 5 1 0 3 0 0 4 5 2 2 3 10 4 23 0 1 1 7 2 7 0 1 4 3 1 0 1 4 1 0 1 2 23 19 13 1 38 53 0 8 0 15 0 0 1 11 2 7 0 0 7 1 0 1 4 3 1 0 2 2 0 5 3 4 2 0 2 4 7 16 0 5 2 2 5 9 1 7 8 22 6 9 3 5 1 0 2 0 0 11 2 11 2 3 9 28 0 12 22 1 0 3 17 1 1 0 0 4 5 2 3 7 0 8 6 2 2 0 1 11 0 6 5 4 3 23 21 1 1 0 1 4 0 4 2 7 3 5 3 0 36 8 47 4 81 69 5 17 24 95 5 13 104 25 15 11 3 4 1 1 7 3 1 7 4 2 0 3 8 1 3 5 0 3 1 1 1 0 3 0 1 0 8 4 5 0 5 2 23 0 0 3 5 9 1 1 0 1 0 1 6 24 7 14 3 4 2 19 0 1 2 1 3 14 1 20 9 16 2 3 12 9 27 16 104 3 39 125 24 134 209 6 2 9 5 33 168 70 408 133 5 1 0 3 0 1 2 2 4 12 6 2 0 2 8 6 2 1 5 1 1 0 0 4 7 1 1 0 0 5 1 3 10 3 4 10 1 4 0 7 1 0 2 1 4 3 1 1 1 1 1 1 0 3 1 0 3 1 0 3 1 1 1 1 1 1 1 1 1 0 2 1 3 4 0 2 11 1 1 1 0 2 3 0 1 5 1 1 1 1 0 0 1 13 1 0 2 1 5 0 0 3 1 11 0 9 22 8 7 17 89 9 140 1 19 5 0 1 0 5 0 1 34 39 1 0 0 7 1 0 3 1 1 1 0 1 0 10 0 0 2 8 3 32 51 51 0 20 78 0 2 6 0 12 7 23 16 10 2 2 0 4 7 0 0 0 12 7 0 3 0 0 1 7 5 12 6 10 2 1 2 4 2 1 17 4 3 10 12 0 12 7 0 0 7 1 1 1 0 2 1 0 8 2 10 3 0 0 7 0 2 3 0 1 1 0 5 8 14 2 60 54 52 21 83 187 94 4 154 51 46 87 65 70 67 409 299 493 115 1113 1986 251 2249 4311 650 3420 2111 5102 1029 416 26929 2202 2590 94 264 4948 394 955 65 180 289 1990 312 237 10 620 1461 98 168 43 22 27 9 6 51 2 15 0 0 4 4 4 3 3 2 19 6 5 4 2 2 1 2 3 9 1 1 0 2 3 1 1 1 0 0 2 0 9 21 11 5 1 6 6 0 9 307 50 18 315 33 9 3 202 378 190 17 214 229 82 1503 286 666 1184 123 414 415 53 162 277 2365 155 907 840 1364 236 172 53 0 9 0 10 1 3 3 4 3 1 1 1 0 3 1 0 0 2 1 8 13 11 30 1 20 15 0 10 5 26 0 10 1 8 25 2 5 0 7 7 0 6 8 0 6 2 6 23 17 86 21 63 8 7 7 1 2 4 19 2 1 27 5 0 0 4 5 0 4 12 1 11 1 1 2 20 20 1 9 0 14 3 1 17 24 10 5 16 9 2 52 14 40 15 5 7 20 12 45 5 0 2 3 0 2 2 3 1 1 0 2 2 2 1 2 5 4 2 3 0 2 1 5 0 2 3 0 3 0 1 1 1 13 4 8 7 0 0 3 1 7 4 7 57 1 0 2 2 1 0 0 15 4 2 13 21 86 19 35 33 47 8 45 84 44 396 93 67 0 23 1 51 194 132 116 81 201 150 24 32 51 194 384 90 5 10 5 3 1 9 0 0 0 2 27 1 1 0 0 5 1 2 2 12 19 10 15 21 13 24 1 3 1 2 11 0 3 27 0 25 5 1 1 0 0 2 3 1 18 28 3 9 1 1 1 0 1 0 2 10 9 11 19 3 3 4 1 5 1 1 0 0 5 5 0 2 2 0 7 0 1 0 5 9 0 8 22 2 2 1 2 4 1 10 4 5 5 0 3 1 0 1 3 2 0 11 9 0 0 3 0 18 2 1 3 0 8 0 3 6 30 6 5 1 43 81 21 8 0 6 0 1 0 8 35 1 10 14 2 0 1 3 10 6 3 46 4 22 74 38 23 4 10 3 1 0 3 0 1 2 7 1 1 0 1 4 3 0 3 0 2 1 3 0 2 15 5 9 1 0 3 1 0 3 1 0 1 4 1 0 2 10 16 5 4 0 4 5 2 7 1 0 2 0 4 3 6 1 7 6 3 4 15 27 29 22 87 1 0 1 4 3 0 1 5 0 3 1 0 0 4 0 11 7 0 4 11 3 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75 20 132 309 334 494 29 210 29 98 558 228 27 7 1 0 16 7 0 3 0 1 1 4 11 1 0 1 1 0 14 3 4 27 0 2 2 1 0 1 18 5 4 3 0 0 4 7 0 2 0 1 1 20 8 7 0 1 1 2 0 5 51 5 1 1 1 0 1 2 7 0 0 5 5 1 0 3 0 2 1 2 6 3 0 2 1 4 3 1 1 0 1 5 0 2 3 0 3 1 1 0 0 6 1 4 0 7 1 0 1 3 1 1 15 3 1 1 4 7 23 24 16 17 7 8 11 0 0 7 1 1 0 3 0 3 0 3 0 0 6 1 2 3 9 1 1 1 1 0 1 2 4 2 11 0 2 0 7 0 2 3 0 0 0 7 6 4 15 17 31 22".split()))

#N=int("20")
#A=list(map(int, "0 0 0 0 0 0 0 0 0 0 0 0 4092 0 7 6 4 15 17 31 22".split()))


N=int(input())
A=list(map(int, input().split()))

ans=0
bef=0

tmp=[]

#20, 25, 33, 35, 48

for i in range(N+1):
    if i==0:
        if A[0]==1:
            bef=0
        elif A[0]>1:
            print("-1")
            exit()
        elif N==0 and A[0]==0:
            print("-1")
            exit()
        else:
            bef=1
        tmp.append(1)
        continue
    elif (bef*2-A[i])>=0:
        bef=bef*2-A[i]
        tmp.append(bef)
    else:
        print("-1")
        exit()

hoge=[]

for i in range(N+1):
    current=A[-(i+1)]
    if i==0:
        bef=current
        ans+=current
        hoge.append(bef)
        continue
    else:
        tmpp = tmp[-(i+1)]
        if bef > tmpp:
            ans+=tmpp+current
            bef=tmpp+current
        else:
            ans+=current+bef
            bef=current+bef
    hoge.append(bef)

if ans==0:
    ans=-1
#print(tmp)
#print(hoge)
print(ans)