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)

#![allow(dead_code)]
#![allow(unused_variables)]
#![allow(unused_variables)]

use std::io::stdin;
use std::str::FromStr;
use std::cmp::min;

fn read<T: FromStr>() -> T {
    let mut str = String::new();
    stdin().read_line(&mut str).ok();
    str.trim().parse().ok().unwrap()
}

fn read_vec<T: FromStr>() -> Vec<T> {
    let mut str = String::new();
    stdin().read_line(&mut str).ok();
    str.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}

fn read_n_vec<T: FromStr>(n: u64) -> Vec<Vec<T>> {
    let mut v_outer = Vec::new();
    for _ in 0..n {
        let v_inner = read_vec();
        v_outer.push(v_inner);
    }
    v_outer
}

fn main() {
    let line: Vec<u64> = read_vec();
    let n = line[0];
    let a = line[1];
    let b = line[2];

    let time = n / (a + b);

    println!("{}", time * a + min(n - time * (a + b), a))
}