A simpler problem: Given an array of integers, find sum of minimum elements of each subset.

Solution: Sort the array so that A[0]<=A[1]<=...<=A[n-1]. Answer= sum 2^(n-i+1)*A[i].

From now on by f(A) we will denote this value for an array.

Prime factorize each number and for each prime p<=10^5 store a list where for each a[i] which is a multiple of p the power of p in a[i] is stored in the list. Let M[p] be this list p.

Answer= product p^f(M[p]) over all primes from 1 to 10^5

f(M[p]) can get quite large so it's advisable to compute it modulo 10^9+6 (because x^109 + 6 = 1 mod 10^9+7.

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