fn gcd(mut a: i64, mut b: i64) -> i64 {
    while b != 0 {
        let t = b;
        b = a % b;
        a = t;
    }

    a
}

fn lcm(a: i64, b: i64) -> i64 {
    (a*b).abs() / gcd(a, b)
}

fn sum_fracts(l: Vec<(i64, i64)>) -> Option<(i64, i64)> {
    if l.is_empty() {
        return None;
    }

    let denom = l.iter().fold(1, |a, b| lcm(a, b.1));

    let (num, den) = l.iter().fold((0, denom), |runner, frac|
            (runner.0 + (frac.0 * denom / frac.1), denom)
    );

    let divisor = gcd(num, den);
    Some((num / divisor, den / divisor))
}