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: Time Limit Exceeded)


using System;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using System.Text;
class Solution
{
    static void Main(String[] args)
    {
     
      var s=Console.ReadLine().Split();
      var n=Convert.ToUInt64(s[0]);
      var a=Convert.ToUInt64(s[1]);
      var b=Convert.ToUInt64(s[2]);
      bool isBlue=true;
      UInt64 answer=0;

        while(n>0){
            
            if(isBlue){
                if(n>=a){
                n-=a;
                answer+=a;

                }else{
                    answer+=(n);
                    n=0;

                }

            }else{
                if(n>=b){
                n-=b;

                }else{
                    n=0;
                }

            }
            isBlue= !isBlue;

        }
        Console.WriteLine(answer);

       
        

           
            
             
 
    }
 
}