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 Rust (1.15.1) (judge verdict: Accepted)

fn count_balls() -> Result<u64, &'static str> {
    let mut input = String::new();
    std::io::stdin().read_line(&mut input)
        .map_err(|_| "input error")?;

    let nab: Vec<u64> = input.trim_right().split_whitespace()
        .map(|n| n.parse::<u64>().unwrap())
        .collect();

    let n = nab[0] / (nab[1] + nab[2]);
    let m = nab[0] % (nab[1] + nab[2]);

    Ok(nab[1] * n + std::cmp::min(m, nab[1]))
}

fn main() {
    println!("{}", count_balls().unwrap());
}