Random chocolates doubt in editorial

[nemesis1]

RANDCHCL - Editorial

PROBLEM LINK: Practice Div-1 Contest Author: Anik Sarker Tester: Raja Vardhan Reddy Editorialist: William Lin DIFFICULTY: Medium PREREQUISITES: Combinatorics PROBLEM: Given an array W of length N, find the expected score from the following process: Choose an integer k between 1 and N uniformly randomly. Let A be k not necessarily distinct elements chosen uniformly randomly and independently from W. Let B be chosen in the same way as A. The score is \sum_{i=1}^k \sum_{j =1}^k \gcd(A_i, B…

this is the link to the editorial where u can even find link to the problem.
In editorialist’s approach
why expected value of gcd(a[i],a[j])*k^2=score?
how expected value term comes from score expression?
Thankyou