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;

fn main() {
    let vs = parse_values::<usize>(3);
    let n = vs[0];
    let a = vs[1];
    let b = vs[2];
    let loop_count = n / (a + b);
    let remain = n % (a + b);
    let remain_a = if a < remain { a } else { remain };
    println!("{}", loop_count * a + remain_a);
}

/// Parse line from io::stdin into T Value
fn parse_line<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

/// Parse whitespace split into T values from io::stdin
fn parse_values<T: std::str::FromStr>(n: usize) -> Vec<T> {
    let line = parse_line::<String>();
    let mut split = line.split_whitespace();
    let mut values = Vec::with_capacity(n);
    for _ in 0..n {
        let v = split.next().unwrap().parse::<T>().ok().unwrap();
        values.push(v);
    }
    values
}