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 (2.13.1) (judge verdict: Time Limit Exceeded)

object Main extends App {
  @scala.annotation.tailrec
  def loop(n: Long, a: Long, b: Long, acc: Long): Long =
    if (n <= 0) acc else if (n < a) acc + n else loop(n - a - b, a, b, acc + a)
  val sc = new java.util.Scanner(System.in)
  val N, A, B = sc.nextLong()
  println(if (A == 0) 0 else loop(N, A, B, 0))
}