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pub fn modcom(n: usize, k: usize, div: usize) -> usize {
    let mut fact = Vec::<usize>::new();
    let mut inv = Vec::<usize>::new();
    let mut finv = Vec::<usize>::new();

    let upper = n + 1;

    fact.resize(upper, 0);
    inv.resize(upper, 0);
    finv.resize(upper, 0);

    fact[0] = 1;
    fact[1] = 1;

    finv[0] = 1;
    finv[1] = 1;

    inv[1] = 1;

    for i in 2..upper {
        fact[i] = fact[i - 1] * i % div;
        inv[i] = div - inv[div % i] * (div / i) % div;
        finv[i] = finv[i - 1] * inv[i] % div;
    }

    fact[n] * (finv[k] * finv[n - k] % div) % div
}

#[cfg(test)]
mod test_combination {
    use crate::math::modcom::modcom;

    #[test]
    fn it_works() {
        assert_eq!(modcom(6, 0, 7), 1);
        assert_eq!(modcom(6, 1, 7), 6);
        assert_eq!(modcom(6, 2, 7), 1);
        assert_eq!(modcom(6, 3, 7), 6);
        assert_eq!(modcom(6, 4, 7), 1);
        assert_eq!(modcom(6, 5, 7), 6);
        assert_eq!(modcom(6, 6, 7), 1);
    }
}