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.Scanner;

/**
 * B - Count Balls
 * 高橋君は青と赤の 2 色のボールを持っており、これらを一列に並べようとしています。
 * 初め、列にボールはありません。
 * 根気のある高橋君は、次の操作を10の100乗 回繰り返します。
 * 列の末尾に、A 個の青いボールを加える。
 * その後、列の末尾に B 個の赤いボールを加える。
 * こうしてできる列の先頭からN 個のボールのうち、青いボールの個数はいくつでしょうか。
 */
public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner( System.in );
        // 先頭から確認するボールの数
        int n = sc.nextInt();
        // 青いボールの数
        int a = sc.nextInt();
        // 赤いボールの数
        int b = sc.nextInt();

        int ballCnt = 0;
        // 青いボールを１つ以上並べている時
        if( a > 0 ) {
            // 繰り返す数を求める
            int divisionAns = n / ( a + b );
            // 繰り返す数を算出した割り算の余りを求める
            int remainderOfDivision = n % ( a + b );

            ballCnt += divisionAns * a;
            ballCnt += remainderOfDivision < a ? remainderOfDivision : a;
        }

        System.out.println( ballCnt );

        sc.close();
    }
}