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
from itertools import accumulate
N = int(input())
As = list(map(int, input().split()))

accR = reversed(list(accumulate(reversed(As))))
num = 1
MAX = 10 ** 13
ans = 0
for a, limit in zip(As, accR):
    tmp = min(num, limit)
    if a > tmp:
        print(-1)
        exit()
    ans += tmp
    num = (tmp - a) * 2
    if num >= MAX:
        num = MAX
print(ans)
