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Converse of Wilsons Theorem

Hi all (in here just assume = is congruent to)

is this a valid proof of the converse of wilsons theorem

show that if m>= 2 is an integer and (m-1)! = -1 mod m then m is prime

what I did was this:

suppose for a contradiction m is not prime so that m = pq for some prime divisor p and some other number q

if (m-1)! = -1 mod m then this implies
(pq-1)! = -1 mod pq
which implies
(pq-1)(pq-2)...(p)...(q)...2*1 = -1 mod pq

but pq | (pq-1)(pq-2)...(p)...(q)...2*1 so should leave remainder 0

contradiction

is this ok? (if it was an exam kind of q?) thanks everyone