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: Wrong Answer)

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
		
		int count=0;
		long blueCount=0;
		long aAmari=0;
		
		Scanner sc=new Scanner(System.in);
		long N=sc.nextLong();
		long A=sc.nextLong();
		long B=sc.nextLong();
		//何回、A+Bの組み合わせが続くか
		long syou=N/(A+B);
		//A+Bのあまり
		long kaisu=N%(A+B);
		
			if(kaisu==0) {
				blueCount=A;
			}else {
				if(kaisu<A) {
					blueCount=(A*syou)+kaisu;
				}else {
				aAmari=kaisu-A;
				if(aAmari<B) {
					blueCount=(A*syou)+A;
				}else {
					aAmari=aAmari-B;
					blueCount=(A*syou)+A+aAmari;
				}
				}
			}
		System.out.println(blueCount);
		
	}
 
}