Problem:
Score : 200 points

Problem Statement

Takahashi has many red balls and blue balls. Now, he will place them in a row.

Initially, there is no ball placed.

Takahashi, who is very patient, will do the following operation 10^{100} times:

Place A blue balls at the end of the row of balls already placed. Then, place B red balls at the end of the row.

How many blue balls will be there among the first N balls in the row of balls made this way?

Constraints

1 \leq N \leq 10^{18}

A, B \geq 0

0 < A + B \leq 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

Print the number of blue balls that will be there among the first N balls in the row of balls.

Sample Input 1

8 3 4

Sample Output 1

4

Let b denote a blue ball, and r denote a red ball. The first eight balls in the row will be bbbrrrrb, among which there are four blue balls.

Sample Input 2

8 0 4

Sample Output 2

0

He placed only red balls from the beginning.

Sample Input 3

6 2 4

Sample Output 3

2

Among bbrrrr, there are two blue balls.

Solution in Scala (2.11.7) (judge verdict: Accepted)

object Main extends App {
  val in = scala.io.Source.stdin.getLines.toSeq
  val ls = in(0).split(' ').map(_.toLong)
  val N = ls(0)
  val A = ls(1)
  val B = ls(2)

  val AB = A + B
  //println(AB)
  val res = N%AB
  //println(res)
  val mod = Math.min(res, A)
  //println(mod)
  val ret = N/AB*A + mod
  println(ret)
}