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: Runtime Error)

fn main() {
    let mut values = read_as_vec().into_iter().map(|s| s.parse::<u32>().unwrap());
    let from_start = values.next().unwrap();
    let blue_ball_cnt = values.next().unwrap();
    let red_ball_cnt = values.next().unwrap();

    if blue_ball_cnt == 0 {
        println!("0");
        return;
    }
    if red_ball_cnt == 0 {
        println!("{}", from_start);
        return;
    }

    let loops = if from_start > 1000 { 1000 } else { from_start };

    let mut all_blues = 0;
    let mut blue_streak = 0;
    let mut red_streak = 0;
    let mut is_current_blue = true;
    for _ in 0..loops {
        if is_current_blue {
            blue_streak += 1;
            all_blues += 1;
            if blue_streak == blue_ball_cnt {
                blue_streak = 0;
                is_current_blue = false;
            }
        } else {
            red_streak += 1;
            if red_streak == red_ball_cnt {
                red_streak = 0;
                is_current_blue = true;
            }
        }
    }
    println!("{}", all_blues);
}
fn read() -> String {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    line.trim().to_string()
}
fn read_as_vec() -> std::vec::Vec<String> {
    read().split(' ').map(|s| s.to_string()).collect()
}