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) {
		// TODO 自動生成されたメソッド・スタブ
		 Scanner sc = new Scanner(System.in);
		 int count=sc.nextInt();
		 int b=sc.nextInt();
		 int r=sc.nextInt();
		 
		 ArrayList<String> ball= new ArrayList();
		 boolean ju=false;
		 while(true){
			 for(int i=0;i<b;i++){
				 ball.add("b");
				 if(ball.size()>count){
					 ju=true;
					 break;
					 }
			 }
			 if(ju)
				 break;
			 
			 for(int i=0;i<r;i++){
				 ball.add("r");
				 if(ball.size()>count){
					 ju=true;
					 break;
					 }
			 }
			 if(ju)
				 break;
		 }
		 
		 int s = 0;
		 for(int i=0;i<count;i++){
			 if(ball.get(i).equals("b"))
				 s++;
		 }
		 System.out.print(s);
	}

}