This morning the jury decided to add one more Very Easy Problem to the Olympiad version. The executive secretary of the Organizing Committee printed its condition in one copy, and now he needs to make
more N copies before the start of the Olympiad. He has two copiers at his disposal, one of which copies a sheet in
x seconds, and the other – for
y.
It is allowed to use both one copier, and both at the same time. You can copy not only from the original, but also from a copy. Help him figure out the minimum time it takes.
Input: The input is three natural numbers
N,
x and
y separated by spaces (
\(1 <= N <= 2 \cdot 10^8,\ 1 <= x, y <= 10\) ).
Output: print a single number – the minimum time in seconds required to obtain
N copies.
Examples
| # |
Input |
Output |
| 1 |
4 1 1 |
3 |
| 2 |
5 1 2 |
4 |