p02665 NOMURA Programming Competition 2020 - 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
```python
n = int(input())
 
a = list(map(int,input().split()))
 
cumsum_a = a.copy()
 
for i in range(n-1, -1, -1):
    cumsum_a[i] += cumsum_a[i+1]
 
ans = 0
node = 1
 
for i in range(n + 1):
    if a[i] > node:
        ans = -1
        break
 
    ans += node
 
    if i < n:
        node = min(2 * (node - a[i]), cumsum_a[i + 1])
 
print(ans)
```