You are given four integers $A$, $B$, $C$, $D$ that satisfy the equations $AmodX=B$ and $CmodX=D$, 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

$13\equiv 1(\mathrm{mod}4)$ and $10\equiv 2(\mathrm{mod}4)$. It can be shown that this is the only possible value of $X$.