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

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.List;
import java.util.StringTokenizer;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Main {
    public static void main(final String[] args) {
        final FastScanner scanner = new FastScanner(System.in);
        final int n = scanner.nextInt();
        final List<Integer> list = IntStream.rangeClosed(0, n)
            .mapToObj(i -> scanner.nextInt())
            .collect(Collectors.toList());

        if (n == 0) {
            if (list.get(0) == 1) {
                System.out.println(1);
            } else {
                System.out.println(-1);
            }
            return;
        }

        if (list.get(0) != 0) {
            System.out.println(-1);
            return;
        }

        final long[] nodes = new long[n + 1];
        nodes[0] = 1;
        for (int depth = 1; depth <= n; depth++) {
            final int leaves = list.get(depth);

            if (leaves > nodes[depth - 1] * 2) {
                System.out.println(-1);
                return;
            }

            nodes[depth] = Math.min(nodes[depth - 1] * 2 - leaves, Long.MAX_VALUE / 2);
        }

        long all = 0;
        long rests = 0;
        for (int depth = n; depth > 0; depth--) {
            final int leaves = list.get(depth);
            all += leaves + rests;
            rests = Math.min(nodes[depth - 1], rests + leaves);
        }

        System.out.println(++all);
    }

    private static class FastScanner {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(final InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (final IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
    }
}
