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
#include <bits/stdc++.h>
using namespace std;

bool chmin(long long &a, long long b) {
	if (a > b) {
		a = b;
		return true;
	}
	return false;
}

int main() {
	int n;
	cin >> n;
	vector<int> a(n + 1);
	for (int i = 0; i < n + 1; i++) {
		cin >> a[i];
	}
	
	vector<long long> b(n + 1, a[n]);
	for (int i = n; i--> 0;) {
		b[i] = b[i + 1] + a[i];
	}
	
	long long v = 1;
	for (int i = 0; i < n + 1; i++) {
		if (chmin(b[i], v)) {
			v = (v - a[i]) * 2LL;
		}
	}
	
	long long ans = 0;
	bool ok = true;
	for (int i = 0; i < n + 1; i++) {
		ok &= (b[i] >= a[i]);
		ans += b[i];
	}
	
	if (not ok) ans = -1;
	
	cout << ans << '\n';
	
	return 0;
}