use std::collections::HashMap;

fn factorial(n: usize) -> usize {
    (1..=n).product()
}

fn binomial_coefficient(p: usize, r: usize) -> usize {
    factorial(p) / (factorial(r) * factorial(p - r))
}

fn prime_factors(n: usize, factors: &mut HashMap<usize, usize>) {
    let mut n = n;
    let mut i = 2;
    while i * i <= n {
        while n % i == 0 {
            *factors.entry(i).or_default() += 1;
            n /= i;
        }
        i += 1;
    }
    if n > 1 {
        *factors.entry(n).or_default() += 1;
    }
}

fn is_binomial_coefficient_possible(p: usize, r: usize, n: usize) -> bool {
    let mut factors = HashMap::new();
    for i in r + 1..=p {
        prime_factors(i, &mut factors);
    }
    for i in 2..=p - r {
        prime_factors(i, &mut factors);
    }
    for (&prime, &count) in &factors {
        if count > n / prime {
            return false;
        }
    }
    true
}

fn main() {
    let n = 10;
    let mut found = false;
    for p in 2.. {
        for r in 0..=p {
            if binomial_coefficient(p, r) == n {
                if is_binomial_coefficient_possible(p, r, n) {
                    println!("p: {}, r: {}", p, r);
                    found = true;
                    break;
                }
            }
        }
        if found {
            break;
        }
    }
}