Once Happy was playing with his friends during his maths class. Seeing this, his teacher asked him to solve a problem. The teacher gave him a set of n positive integers and asked him to tell the sum of the product of elements of all the possible subsets.

For e.g. Say, the teacher gave him a set {2, 3, 5}. The possible subsets of this set are {2}, {3}, {5}, {2, 3}, {2, 5}, {3, 5} and {2, 3, 5}. So Happy should report the answer as the sum of 2, 3, 5, 6 (2 * 3), $10$ (2 * 5), $15$ (3 * 5) and $30$ (2 * 3 * 5) i.e., $71$ to the teacher.

As the output of the problem can be large, so the teacher asked happy to report the answer modulo $10^9$+7 ($1000000007$).

INPUT:

The first line of input contains an integer n denoting the number of elements in the set and the next line consists of n space separated integers. The i^th integer is denoted by a_i.

OUTPUT:

Print the answer modulo $10^9$+7 ($1000000007$).

Constraints:

1 ≤ n ≤ $10^5$
0 ≤ a_i ≤ $10^7$