Surprise me!

题目描述

Tired of boring dates, Leha and Noora decided to play a game. Leha found a tree with $n$ vertices numbered from $1$ to $n$ . We remind you that tree is an undirected graph without cycles. Each vertex $v$ of a tree has a number $a_{v}$ written on it. Quite by accident it turned out that all values written on vertices are distinct and are natural numbers between $1$ and $n$ . The game goes in the following way. Noora chooses some vertex $u$ of a tree uniformly at random and passes a move to Leha. Leha, in his turn, chooses (also uniformly at random) some vertex $v$ from remaining vertices of a tree $(v≠u)$ . As you could guess there are $n(n-1)$ variants of choosing vertices by players. After that players calculate the value of a function $f(u,v)=φ(a_{u}·a_{v})$ $·$ $d(u,v)$ of the chosen vertices where $φ(x)$ is Euler's totient function and $d(x,y)$ is the shortest distance between vertices $x$ and $y$ in a tree. Soon the game became boring for Noora, so Leha decided to defuse the situation and calculate expected value of function $f$ over all variants of choosing vertices $u$ and $v$ , hoping of at least somehow surprise the girl. Leha asks for your help in calculating this expected value. Let this value be representable in the form of an irreducible fraction ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF809E/2c40be71c60fe708ee9e4e80e2cd7a26163f3bd6.png). To further surprise Noora, he wants to name her the value ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF809E/e621f869f3b1e6ca6c81000c1f17dc3c0088747c.png). Help Leha!

输入输出格式

输入格式

The first line of input contains one integer number $n$ $(2<=n<=2·10^{5})$ — number of vertices in a tree. The second line contains $n$ different numbers $a_{1},a_{2},...,a_{n}$ $(1<=a_{i}<=n)$ separated by spaces, denoting the values written on a tree vertices. Each of the next $n-1$ lines contains two integer numbers $x$ and $y$ $(1<=x,y<=n)$ , describing the next edge of a tree. It is guaranteed that this set of edges describes a tree.

输出格式

In a single line print a number equal to $P·Q^{-1}$ modulo $10^{9}+7$ .

输入输出样例

输入样例 #1

3
1 2 3
1 2
2 3


输出样例 #1

333333338


输入样例 #2

5
5 4 3 1 2
3 5
1 2
4 3
2 5


输出样例 #2

8


说明

Euler's totient function $φ(n)$ is the number of such $i$ that $1<=i<=n$ ,and $gcd(i,n)=1$ , where $gcd(x,y)$ is the greatest common divisor of numbers $x$ and $y$ . There are $6$ variants of choosing vertices by Leha and Noora in the first testcase: - $u=1$ , $v=2$ , $f(1,2)=φ(a_{1}·a_{2})·d(1,2)=φ(1·2)·1=φ(2)=1$ - $u=2$ , $v=1$ , $f(2,1)=f(1,2)=1$ - $u=1$ , $v=3$ , $f(1,3)=φ(a_{1}·a_{3})·d(1,3)=φ(1·3)·2=2φ(3)=4$ - $u=3$ , $v=1$ , $f(3,1)=f(1,3)=4$ - $u=2$ , $v=3$ , $f(2,3)=φ(a_{2}·a_{3})·d(2,3)=φ(2·3)·1=φ(6)=2$ - $u=3$ , $v=2$ , $f(3,2)=f(2,3)=2$ Expected value equals to ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF809E/fd763e469519b65bfd50af11acb740e2ea841c2a.png). The value Leha wants to name Noora is $7·3^{-1}=7·333333336=333333338$ ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF809E/23c9d8b560378dc3e1bda3c6cf2ad52a14105af7.png). In the second testcase expected value equals to ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF809E/cfbdadeb4c85e39ef43a1fbfa72abe8eae49472c.png), so Leha will have to surprise Hoora by number $8·1^{-1}=8$ ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF809E/23c9d8b560378dc3e1bda3c6cf2ad52a14105af7.png).