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)

use std::io::stdin;

fn main() {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    let mut line = buf.split_whitespace();
    let n: u64 = line.next().unwrap().parse().unwrap();
    let blue: u64 = line.next().unwrap().parse().unwrap();
    let red: u64 = line.next().unwrap().parse().unwrap();

    println!("{}", solve(n, blue, red));
}

fn solve(n: u64, blue: u64, red: u64) -> u64{
    let quotient = n / (blue + red);
    let surplus = n % (blue + red);
    return  match surplus {
        surplus if surplus >= blue => quotient * blue + blue,
        surplus if surplus < blue => quotient * blue + surplus,
        _ => unreachable!()
    }
}