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::cmp::{max, min};
use std::io::stdin;
use std::str::FromStr;

fn main() {
    let (n, a, b) = input_three::<i64>().unwrap();

    let ans = n / (a + b) * a + min(n % (a + b), a);
    println!("{}", ans);
}

fn input<T: FromStr>() -> Result<T, T::Err> {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    Ok(buf.trim().parse().ok().unwrap())
}

fn input_vec<T: FromStr>() -> Result<Vec<T>, T::Err> {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    Ok(buf
        .trim()
        .split_whitespace()
        .map(|x| x.parse().ok().unwrap())
        .collect::<Vec<_>>())
}

fn input_two<T: FromStr>() -> Result<(T, T), T::Err> {
    let tmp = input_vec::<String>().unwrap();
    Ok((tmp[0].parse()?, tmp[1].parse()?))
}

fn input_three<T: FromStr + Clone>() -> Result<(T, T, T), T::Err> {
    let tmp = input_vec::<T>().ok().unwrap();
    // println!("{:?}", tmp);
    Ok((tmp[0].clone(), tmp[1].clone(), tmp[2].clone()))
}