import "utils/casts/u32_to_field" as to_field

// Binomial Coeffizient, n!/(k!*(n-k)!).
def fac(field x) -> field:
    field f = 1
    field counter = 0
    for u32 i in 1..100 do
        f = if counter == x then f else f * to_field(i) fi
        counter = if counter == x then counter else counter + 1 fi
    endfor
    return f

def main(field n, field k) -> field:
    return fac(n)/(fac(k)*fac(n-k))