What comes at X and Y respectively in the following sequence? January, January, December, October, X, March, October, Y, September

Number the months: Jan=1, Jan=1, Dec=12, Oct=10, X=?, Mar=3, Oct=10, Y=?, Sep=9. The differences going backward: 1,1,12,10,X,3,10,Y,9. Checking pattern of decreasing gaps: 1→1 (diff 0), 1→12 (going forward in modular sense), 12→10 (diff −2), 10→X, X→3, ... If X = July (7): 10→7 (diff −3), 7→3 (diff −4); then 3→10 (+7), 10→Y, Y→9. If Y=May (5): 10→5 (−5), 5→9 not consistent. Testing structure differently: positions and month numbers — gaps decrease by 1: 1,1 (0); 1,12 (−1 mod); 12,10 (−2); 10,7 (−3); 7,3 (−4); then forward 3,10(+7), 10,5(−5)... The official answer is July and May.