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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
class Ho{
  static void Main(){
    var aho = Console.ReadLine().Split();
    var N = long.Parse(aho[0]);
    var A = long.Parse(aho[1]);
    var B = long.Parse(aho[2]);
    if(N < A){
      Console.WriteLine(N);
      return;
    }
    long goukei = A+B;
    long amari = N%goukei;
    long setto = (N-amari)/goukei*A;
    if(amari >= A){
      Console.WriteLine(setto+A);
    }
    else{
      Console.WriteLine(setto+amari);
    }
  }
}