import Data.List (foldl1') --'

foldl1_ = foldl1' --'

multOrder a m
  | gcd a m /= 1 = error "Arguments not coprime"
  | otherwise = foldl1_ lcm $ map (multOrder_ a) $ primeFacsExp m

multOrder_ a (p, k) = r
  where
    pk = p ^ k
    t = (p - 1) * p ^ (k - 1) -- totient \Phi(p^k)
    r = product $ map find_qd $ primeFacsExp t
    find_qd (q, e) = q ^ d
      where
        x = powerMod pk a (t `div` (q ^ e))
        d = length $ takeWhile (/= 1) $ iterate (\y -> powerMod pk y q) x