Luka started driving international routes with his truck. His biggest problem is the border with Slovenia. The border is a point of entrance into the European Union, so every truck is thoroughly examined. Because of this, Luka always has to wait several hours there. To kill the time, he comes up with various logic and math games.
In one of them, Luka first reads the numbers off of license plates and writes them down on a piece
of paper. Then he tries to find an integer
greater than
such that all integers on the paper give the
same remainder when divided by
. Luka tries to find as many such integers
as possible.
Write a program that, given Luka's
integers, determines all such integers
.
Input Specification
The first line contains the integer
, the number of integers on paper.
Each of the following lines contains one integer between
and
(one billion). All these
integers will be distinct.
The input data will guarantee that at least one integer will always exist.
Output Specification
Output all integers separated by spaces, in any order.
Scoring
In test cases worth points, each of the
numbers will be at most
.
Sample Input 1
3
6
34
38
Sample Output 1
2 4
Sample Input 2
5
5
17
23
14
83
Sample Output 2
3
In the first example, all integers give a remainder of when divided by
and the remainder
when
divided by
.
Comments
Please check the judge of this problem.
For this problem, you must not have any trailing spaces in your output and each line must terminate with a newline (
\n
).Thanks for help!