i am stuck at simple problem , and the problem is that there is no Editorial available for this problem.

The problem is as follows:

Given M (Distinct) integers A1 , A2 , A3 , A4 , A5 ...... , Am , find all integers K , such that remainder of all elements with k is same I.E. A1%K = A2%K = A3%K = ..... = Am%K

and K>1.

Number of elements are 100 , and Ai <= 10^9

My solution is brute force: i am running a loop from 2 to second largest element (which can be upto 10^9) and finding all k , but its giving TLE.

This is the link to the problem

any hint or help would be appreciative. Thanks in advance and happy coding.