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: Time Limit Exceeded)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
fn main() {
    let mut values = read_as_vec().into_iter().map(|s| s.parse::<u64>().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 mut all_blues = 0;
    let mut blue_streak = 0;
    let mut red_streak = 0;
    let mut is_current_blue = true;
    for _ in 0..from_start {
        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()
}
*/

fn main() {
    let exe = "/tmp/bin0D9D7310";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";