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 Kotlin (1.3.71) (judge verdict: Runtime Error)

fun main (args:Array<String>) {
    var (allBalls, bBall, rBall) = readLine()!!.split(" ").map(String::toInt)
    var blueBall = 0

    if(bBall + rBall == allBalls){
        print(bBall)
        return
    }
    if(bBall + rBall > allBalls){
        if(bBall <= allBalls){
            print(bBall)
            return
        }
        else{
            print(bBall)
            return
        }
    }
    if(bBall == 0){
        print(0)
        return
    }
    while(allBalls > 0){
        allBalls -= bBall
        allBalls -= rBall
        blueBall += bBall
    }
    println(blueBall)
}