Very Simple Problem

This morning the jury decided to add to the Olympiad one more problem Very Simple Problem. The executive Secretary of the Organizing Committee published its condition in one instance, and now he needs before the start of the Olympiad to make n copies more. He has two copy machines, the first one can make a copy of one paper for х seconds, the other one makes a copy for y seconds. You may use either any one copy machine, or both simultaneously. You can make a copy not only from the original, but also from the copy.

Help him to find out what is the minimum time it will take.

Input

Three positive integers n, x и y (1 ≤ n ≤ 2 ∙10^8, 1 ≤ x, y ≤ 10).

Output

Print one number - the minimum time in seconds to get n copies.

Examples