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(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int a = sc.nextInt(); // 青のボール
        int b = sc.nextInt();
        String balls = "";
        String flg = "a";
        
        while(balls.length() <= n){
            if(flg.equals("a")){
                for(int i=0; i<a; i++){
                    balls += "a";
                }
                flg = "b";
            }
            else{
                for(int i=0; i<b; i++){
                    balls += "b";
                }
                flg = "a";
            }
        }
        
        balls = balls.substring(0, n+1);
        
        int ans = 0;
        for(int i=0; i<n; i++){
            if(balls.charAt(i) == 'a'){
                ans++;
            }
        }
        
        System.out.println(ans);
    }
}