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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scan s = new Scan();
        long N = s.nL();
        long A = s.nL();
        long B = s.nL();
        if(A == 0){
            System.out.println(0);
        }else{
            long rest = N % (A+B);
            long result = rest - A <= 0 ? A * (N / (A+B)) + rest : A * (N / (A+B)) + A;
            System.out.println(result);
        }
    }
    
    static class Scan{
        private static Scanner sc = new Scanner(System.in);
        public static int nI(){
            return Integer.parseInt(sc.next());
        }
        public static long nL(){
            return Long.parseLong(sc.next());
        }
        public static String nS(){
            return sc.next();
        }
        public static double nD(){
            return Double.parseDouble(sc.next());
        }
    }
}