A8811 | Little Elephant and LCM

The Little Elephant loves the LCM (least common multiple) operation of a non-empty set of positive integers. The result of the LCM operation of $k$ positive integers $x_{1},x_{2},...,x_{k}$ is the minimum positive integer that is divisible by each of numbers $x_{i}$ .

Let's assume that there is a sequence of integers $b_{1},b_{2},...,b_{n}$ . Let's denote their LCMs as $lcm(b_{1},b_{2},...,b_{n})$ and the maximum of them as $max(b_{1},b_{2},...,b_{n})$ . The Little Elephant considers a sequence $b$ good, if $lcm(b_{1},b_{2},...,b_{n})=max(b_{1},b_{2},...,b_{n})$ .

The Little Elephant has a sequence of integers $a_{1},a_{2},...,a_{n}$ . Help him find the number of good sequences of integers $b_{1},b_{2},...,b_{n}$ , such that for all $i$ $(1<=i<=n)$ the following condition fulfills: $1<=b_{i}<=a_{i}$ . As the answer can be rather large, print the remainder from dividing it by $1000000007$ $(10^{9}+7)$ .

The first line contains a single positive integer $n$ $(1<=n<=10^{5})$ — the number of integers in the sequence $a$ . The second line contains $n$ space-separated integers $a_{1},a_{2},...,a_{n}$ $(1<=a_{i}<=10^{5})$ — sequence $a$ .

In the single line print a single integer — the answer to the problem modulo $1000000007$ $(10^{9}+7)$ .