Check whether it accepts a finite determinant automaton at least one word of length k, if so - print it, else - print "No"

Question

I wrote data structure and some functions for automata, but I stuck with find_way function that will accept automata object and k.

type FSM q = ([q], Alphabet, [Transition q], q, [q])
type Alphabet = [Char]
type Transition q = (q, Char, q)

states :: FSM q -> [q]
states (u, _, _, _, _) = u

alph :: FSM q -> Alphabet
alph (_, a, _, _, _) = a
trans :: FSM q -> [Transition q]
trans (_, _, t, _, _) = t
start :: FSM q -> q
start (_, _, _, s, _) = s
final :: FSM q -> [q]
final (_, _, _, _, f) = f

--return a or Nothing if no transition found
delta :: Eq a => FSM a -> a -> Char -> Maybe a
delta m st symbol = listToMaybe [q1 | (q0, x, q1) <- trans m, q0 == st, x == symbol]

--return "No" or first accepted word found
    
goal:: Eq a => FSM a -> Int -> String
goal m k = fromMaybe "No" $ asum [find_way m k x | x <- alph m]

find_way :: Eq a => FSM a -> Int -> Char -> Maybe String