You are given four integers ~A~, ~B~, ~C~, ~D~ that satisfy the equations ~A \bmod X = B~ and ~C \bmod X = D~, where ~X~ is a positive integer. Output all possible values of ~X~. It is possible that there are none — in which case you do not need to output anything.

Constraints

For all subtasks:

• ~1 \le A, B, C, D \le 10^{12}~
• ~B < A~ and ~D < C~

Points Awarded	Additional Constraints
3 points	~A = C~ and ~B = D~
5 points	~1 \le A, B, C, D \le 10^6~
7 points	No further constraints

Input Specification

The only line of input contains four integers ~A~, ~B~, ~C~ and ~D~.

Output Specification

Output all possible values of ~X~, each on their own line and in ascending order.

Sample Input

13 1 10 2

Sample Output

4

Explanation for Sample

~13 \equiv 1 \pmod{4}~ and ~10 \equiv 2 \pmod{4}~. It can be shown that this is the only possible value of ~X~.