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.ArrayList;
import java.util.Scanner;

public class Main {
  public static void main(String[] args ) throws Exception {
    Scanner sc = new Scanner(System.in);
    String input = sc.nextLine();
    String frontBall = input.substring(0,input.indexOf(" "));
    String afterFrontBall = input.substring(input.indexOf(" ")+1);
    int Front = Integer.parseInt(frontBall);
    String blue = afterFrontBall.substring(0,afterFrontBall.indexOf(" "));
    String afterBlueBall = afterFrontBall.substring(afterFrontBall.indexOf(" ")+1);
    int blueBall = Integer.parseInt(blue);
    String red = afterBlueBall;
    int redBall = Integer.parseInt(red);
    // System.out.println(Front);
    // System.out.println(blue);
    // System.out.println(red);


    ArrayList<String> balls = new ArrayList<String>(Front);
    boolean add = true;
    while(add) {
    for(int i = 0;i < blueBall;i++) {
    	balls.add("b");
    // 	System.out.println(balls.get(balls.size()-1));
    // 	System.out.println(balls.size());
    // 	System.out.println(Front);
    	if(balls.size() == Front) {
    	    add = false;
    	    break;
    	}
    }
    for(int i = 0;i < redBall;i++) {
    	balls.add("r");
    // 	System.out.println(balls.get(balls.size()-1));
    // 	System.out.println(balls.size());
    // 	System.out.println(Front);
    	if(balls.size() == Front) {
    	    add = false;
    	    break;
    }

    }
    }

    // 切り出して、数える
    int count = 0;
    for(int i = 0;i < Front;i++) {
    	if(balls.get(i).equals("b")) count++;
    // 	System.out.print(balls.get(i));
    }
    System.out.println(count);

  }
  }