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: Wrong Answer)

// Template from https://techracho.bpsinc.jp/jhonda/2019_08_05/78537

// input macro for competive-programming from https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        input_inner!{$s, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };

    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, bytes) => {
        read_value!($iter, String).into_bytes()
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

fn main() {
    use std::io::Read;
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();

    println!("{}", solve(&s));
}

macro_rules! test {
    ($($exp_input:expr => $output:expr),* $(,)*) => {
        #[test]
        fn solve_test() {
            $(
                let start = std::time::Instant::now();
                let input = solve($exp_input);
                let end = start.elapsed();
                assert_eq!(input, $output, "{}.{:03}", end.as_secs(), end.subsec_millis());
                assert!(end.as_secs() <= 2, "expected_sec: {}sec, actual_sec: {}sec", 2, end.as_secs());
                assert!(end.as_secs() <= 1, "expected_sec: {}sec, actual_sec: {}sec", 1, end.as_secs());
                assert!(end.subsec_millis() <= 10, "expected_ms: {}ms, actual_ms: {}ms", 10, end.subsec_millis());
                // assert!(end.subsec_millis() <= 2, "expected_ms: {}ms, actual_ms: {}ms", 2, end.subsec_millis());
            )*
        }
    };
}

test! {
r#"8 3 4"# => r#"4"#,

r#"8 0 4"# => r#"0"#,

r#"6 2 4"# => r#"2"#,

}

fn solve(src: &str) -> String {
    let mut src_iter = src.split_whitespace();
    input! {
        source = src_iter,
        mut n: usize,
        a: usize,
        b: usize,
    }

    let mut ans = 0;
    let mut flag = true;

    loop {
        let x = if flag { a } else { b };
        if n >= x {
            n = n - x;
            ans += if flag { x } else { 0 };
        } else {
            ans += n;
            break;
        }
        flag = !flag;
    }

    ans.to_string()
}