Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Joty and Chocolate

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLittle Joty has got a task to do. She has a line of *n* tiles indexed from 1 to *n*. She has to paint them in a strange pattern.

An unpainted tile should be painted Red if it's index is divisible by *a* and an unpainted tile should be painted Blue if it's index is divisible by *b*. So the tile with the number divisible by *a* and *b* can be either painted Red or Blue.

After her painting is done, she will get *p* chocolates for each tile that is painted Red and *q* chocolates for each tile that is painted Blue.

Note that she can paint tiles in any order she wants.

Given the required information, find the maximum number of chocolates Joty can get.

Input

The only line contains five integers *n*, *a*, *b*, *p* and *q* (1 ≤ *n*, *a*, *b*, *p*, *q* ≤ 10^{9}).

Output

Print the only integer *s* — the maximum number of chocolates Joty can get.

Note that the answer can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.

Examples

Input

5 2 3 12 15

Output

39

Input

20 2 3 3 5

Output

51

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/23/2018 23:47:23 (d2).

Desktop version, switch to mobile version.

User lists

Name |
---|