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
N = int(input())
A = [int(i) for i in input().split()]

L, R = [A[-1]], [A[-1]]
for i in range(1, N+1):
    L.append((L[-1]+1)//2+A[-1-i])
    R.append((R[-1]+A[-1-i]))
L = L[::-1]
R = R[::-1]

if L[0] >= 2:
    print(-1)
    exit()

ans = 1
p = 1
for i in range(1, N+1):
    ans += min(p*2, R[i])
    p = min(p*2, R[i])-A[i]
print(ans)
