#D6933. Folia
Folia
Folia
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.
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.
Examples
Input
3 0 1 1 2
Output
7
Input
4 0 0 1 0 2
Output
10
Input
2 0 3 1
Output
-1
Input
1 1 1
Output
-1
Input
10 0 0 1 1 2 3 5 8 13 21 34
Output
264
inputFormat
input are integers.
Input
Input is given from Standard Input in the following format:
N A_0 A_1 A_2 \cdots A_N
outputFormat
Output
Print the answer as an integer.
Examples
Input
3 0 1 1 2
Output
7
Input
4 0 0 1 0 2
Output
10
Input
2 0 3 1
Output
-1
Input
1 1 1
Output
-1
Input
10 0 0 1 1 2 3 5 8 13 21 34
Output
264
样例
4
0 0 1 0 210