## Problem

Minka is very smart kid who recently started learning computer programming.

His coach gave him a cyclic array A having N numbers, and he has to perform Q operations on this array.

In each operation the coach would provide him with a number X. After each operation, every element of the cyclic array would be replaced by the sum of itself and the element lying X positions behind it in the cyclic array. All these replacements take place simultaneously.

For example, if the cyclic array was [a, b, c, d], then after the operation with X = 1, the new array would be [a+d, b+a, c+b, d+c].

He needs to output the sum of the elements of the final array modulus 10^9+7.

He made a program for it but it’s not very efficient. You know he is a beginner, so he wants you to make an efficient program for this task because he doesn’t want to disappoint his coach.

**Input**

The first line of each test file contains a integer N (1 <= N <= 100000).

The next line contains N space separated integers which represent the elements of the cyclic array ( 1 <= Ai <= 10^9 ).

The third line contains a integer Q (0 <= Q <= 1000000) representing the number of operations that will be applied to the array.

Finally, Q lines follow, each one containing an integer X (0 <= X < N).

**Output**

Your program should output to the standard output stream the **sum of the elements of the final array modulus 10^9+7.**

*Note: There is a newline character at the end of the last line of the output.*

**Sample Input 1**

```
5
1 2 3 4 5
2
1
0
```

**Sample Output 1**

```
60
```

**Explanation of Sample Input 1**

- After the 1st operation (X = 1), the array would be [1+5, 2+1, 3+2, 4+3, 5+4] =

[6, 3, 5, 7, 9] - After 2nd operation (X = 0), the array would be [6+6, 3+3, 5+5, 7+7, 9+9] =

[12, 6, 10, 14, 18] - Thus the correct answer would equal to = (12+6+10+14+18) % (10^9+7) = 60

**Sample Input 2**

```
5
1 2 3 4 5
0
```

**Sample Output 2**

`15 `

My Solution 🙂

__author__ = 'Rajind' from sys import stdin arr = [] n = int(stdin.readline()) line = stdin.readline() arr = map(int, line.split()) q = int(stdin.readline()) arrsum = sum(arr) result = (2**q)*arrsum % (10**9+7) print result

~Rajind Ruparathna