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 static System.Console;
using System.Linq;

namespace AC
{
   public class shiokara
   {
      static void Main(string[] args)
      {
          long[] n = new long[3];
          n =　ReadLine().Split(' ').Select(long.Parse).ToArray();

          if(n[1] == 0){
              WriteLine(0);
              return;
          }else if(n[2] == 0){
              WriteLine(n[0]);
              return;
          }

          long ans1 = n[0] / (n[1] + n[2]);
          long ans2 = n[0] % (n[1] + n[2]);
          long ans = 0;
          if(ans2 <= n[1]){
              ans = ans1 * n[1] + ans2;
          }else{
              ans = ans1 * n[1] + n[1];
          }
          WriteLine(ans);
      }
   }
}