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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        C_Folia solver = new C_Folia();
        solver.solve(1, in, out);
        out.close();
    }

    static class C_Folia {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            long maxAtDepth = 1;
            long[] inner = new long[n + 1];
            long[] leaves = new long[n + 1];
            final long infinity = Long.MAX_VALUE / 2 - 100;
            for (int i = 0; i <= n; i++) {
                leaves[i] = in.nextInt();
                if (maxAtDepth < leaves[i]) {
                    out.println(-1);
                    return;
                }
                inner[i] = maxAtDepth - leaves[i];
                maxAtDepth = Math.min(infinity, 2 * inner[i]);
            }
            inner[n] = 0;
            for (int i = n - 1; i >= 0; i--) {
                inner[i] = Math.min(inner[i], inner[i + 1] + leaves[i + 1]);
            }

            long ans = 0;
            for (int i = 0; i <= n; i++) {
                ans += leaves[i];
                ans += inner[i];
            }
            out.println(ans);
        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

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

    }
}

