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: Runtime Error)

import java.util.*;

public class Main {
	public static void main(final String[] args) {

        Scanner sc = new Scanner(System.in);

        // ボールの総数
        long n = sc.nextInt();

        // 末尾に加えた青いボールの数
        long a = sc.nextInt();

        // 末尾に加えた赤いボールの数
        long b = sc.nextInt();

        // 青いボールを加えた回数
        long num = (n / (a + b)) * a;

        // それ以外の青いボールの数
        long rem = n % (a + b);

        num += Math.max(a, rem);

        // 出力
        System.out.println(num);
    }
}