dsalgo 0.3.7

use crate::{
    accumulate::accumulate,
    factorial::factorial,
    multiplicative_inverse::MulInv,
};

pub fn inverse_factorial_table<T>(size: usize) -> Vec<T>
where
    T: std::ops::Mul<Output = T> + MulInv<Output = T> + From<u64> + Clone,
{
    if size == 0 {
        return vec![];
    }
    let mut v = (0..size as u64).map(|i| (i + 1).into()).collect::<Vec<T>>();
    if size == 0 {
        return v;
    }
    v[size - 1] = factorial::<T>(size as u64 - 1).mul_inv();
    let op = |a: T, b: T| -> T { a * b };
    let mut ifact = accumulate(&op, v.into_iter().rev()).collect::<Vec<_>>();
    ifact.reverse();
    ifact
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test() {
        use crate::{
            default_static_modular_arithmetic::Modular1_000_000_007,
            static_modular_int::StaticModularInt,
        };

        type Mint = StaticModularInt<u32, Modular1_000_000_007>;

        let res = inverse_factorial_table::<Mint>(20)
            .into_iter()
            .map(|x| x.value())
            .collect::<Vec<u32>>();
        assert_eq!(
            res,
            [
                1, 1, 500000004, 166666668, 41666667, 808333339, 301388891,
                900198419, 487524805, 831947206, 283194722, 571199524,
                380933296, 490841026, 320774361, 821384963, 738836565,
                514049213, 639669405, 402087866
            ],
        );
    }
}