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.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.StringTokenizer;

class Main {
    static final int MOD = 1000000007;
    static final int INF = 1 << 30;
    static final int ALF = 26;

    Main() {
        FastScanner sc = new FastScanner(System.in);
        long ans = 0;
        int N = sc.nextInt();
        int[] A = sc.nextIntArray(N + 1);
        long[] ables = new long[N + 1];
        ables[N] = A[N];
        for (int i = N - 1; i >= 0; i--) {
            ables[i] = A[i] + ables[i + 1];
        }
        if (A[0] > 1) {
            System.out.println(-1);
            return;
        }
        long prebranch = A[0] == 1 ? 0 : 1;
        long branch;
        long leaf;
        ables[0] = 1;
        for (int i = 1; i <= N; i++) {
            if (A[i] <= prebranch * 2) {
                long next = Math.min(ables[i], prebranch * 2);
                leaf = A[i];
                branch = next - leaf;
                ables[i] = leaf + branch;
                prebranch = branch;
            } else {
                System.out.println(-1);
                return;
            }
        }
        for (int i = 0; i <= N; i++) {
            ans += ables[i];
        }
        System.out.println(ans);
        System.err.println(Arrays.toString(ables));
    }

    public static void main(String[] args) {
        new Main();
    }
}

class FastScanner {
    private BufferedReader reader = null;
    private StringTokenizer tokenizer = null;

    public FastScanner(InputStream in) {
        reader = new BufferedReader(new InputStreamReader(in));
        tokenizer = null;
    }

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

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

        return tokenizer.nextToken("\n");
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

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

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public ArrayList<Integer> nextIntList(int n) {
        ArrayList<Integer> a = new ArrayList<Integer>(n);
        for (int i = 0; i < n; i++)
            a.add(nextInt());
        return a;
    }

    public ArrayList<Long> nextLongList(int n) {
        ArrayList<Long> a = new ArrayList<Long>(n);
        for (int i = 0; i < n; i++)
            a.add(nextLong());
        return a;
    }

    public int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    public long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nextLong();
        return a;
    }
}