Hurry up

Time Limit: 1000ms

Memory Limit: 256MB

B - Hurry up

Submissions Submit

Robbing Balloons composition's problem-set contains $N$ problems.
The cat "Kitty" with her friend, the dog "Lucy" want to participate as a team in the competition.
If Kitty needs $X$ minutes to solve a single problem and Lucy needs $Y$ minutes to do so, what is the minimum time required by their team to solve all problems?
Please note that each one of them has a laptop and can solve the problems separately. If one of them solved a certain problem, no need to solve it again by the other one, as they are a team!

Input

The first and only line contains three integers $N$, $X$ and $Y$ ($1 \le N, X, Y \le 10^9$), the number of problems, the number of minuets Kitty needs to solve a single problem and the number of minuets Lucy needs to solve a single problem.

Output

Print a single integer, the minimum number of minutes Kitty and Lucy team needs to solve all problems.

Notes

In the first sample, we have 10 problems. Kitty and Lucy will start to solve the problems when the competition starts. Kitty can solve a problem in each 2 minutes, while Lucy can solve a problem in each 3 minutes. In 12 minutes, Kitty will solve 6 problems and Lucy will solve 4. So, their team can solve 10 problems in 12 minutes and this is the minimum time they need to solve all 10 problems.

Samples

Input	Output
10 2 3 Copy	12 Copy

We have 2 solutions for this problem:
Firts solution is to use binary search on the answer, if we assume that $z$ is the answer, then we can tell how much problems Kitty can solve and how much problems Lucy can solve, if both are enough to solve all $n$ problems then $z$ is a possible answer.
Second solution is to use math, lets say we want Kitty to solve $a$ problems, then Lucy has to solve $n-a$ problems, if Kitty will take a lot of time solving $a$ problems while Lucy won't take that much time then we should try and decrease $a$ and give Lucy more problems to solve. Generally speaking, we want to minimise the difference between the time Kitty will take to solve her problems and the time Lucy will take, the best possible case is to have both Kitty and Lucy take the same amount of time to solve the $n$ problems, that is $aX - (n-a)Y = 0$, this is an equation with one unknown variable and can be solved, if $a$ turns out to be an integer then giving Kitty $a$ problems is the best solution, if it's not an integer then the best solution will be either $\lfloor a \rfloor$ or $\lceil a \rceil$, we should try both of them and choose the better option.