codeforces 787a

听说这其实就是一道水题，我硬生生用了数论方法来解，真是蠢。主要是因为跟青蛙的约会这道题很相似，直接套模板就过了。

关于青蛙的约会（poj 1061）我写的题解：http://blog.csdn.net/qq1059752567/article/details/53384273

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A. The Monster

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

A monster is chasing after Rick and Morty on another planet. They're so frightened that sometimes they scream. More accurately, Rick screams at times b, b + a, b + 2a, b + 3a, ... and Morty screams at times d, d + c, d + 2c, d + 3c, ....

The Monster will catch them if at any point they scream at the same time, so it wants to know when it will catch them (the first time they scream at the same time) or that they will never scream at the same time.

Input

The first line of input contains two integers a and b (1 ≤ a, b ≤ 100).

The second line contains two integers c and d (1 ≤ c, d ≤ 100).

Output

Print the first time Rick and Morty will scream at the same time, or  - 1 if they will never scream at the same time.

Examples

input

20 2
9 19

output

82

input

2 1
16 12

output

-1