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.util.Scanner;
public class Main {


    public static void main(String[] args) {


        Scanner scan = new Scanner(System.in);
        int N= scan.nextInt();
        long A[]=new long[N+1];
        long MAX=0;
    for(int i=0;i<=N;i++){A[i]=scan.nextLong();
    MAX=MAX+A[i];}
    long NE=1;
    long P=0;
if(MAX==0){NE=-1;}
    for(int i2=0;i2<=N&&NE>=0;i2++){P=P+NE;
   NE=NE-A[i2];
MAX=MAX-A[i2];
        NE=NE*2;
        if(NE>MAX){NE=MAX;}

    }
    if(NE<0){P=-1;}
    System.out.println(P);
    }
}
