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 main() {
    let (n, a, b) = input();
    println!("{}", solve(n, a, b));
}

fn input() -> (usize, usize, usize) {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    buf.pop();
    let mut iter = buf.split_whitespace();
    let n: usize = iter.next().unwrap().parse().unwrap();
    let a: usize = iter.next().unwrap().parse().unwrap();
    let b: usize = iter.next().unwrap().parse().unwrap();
    (n, a, b)
}

fn solve(n: usize, a: usize, b: usize) -> usize {
    let c = (n / (a+b));
    let d = n - c * (a + b);
    if d < a {
        return a * c + d
    }
    a * (c + 1)
}