Ok, I went through analysis, and I am 80% sure that this is illegal due to impossible promotion.
4Q3/1Q5Q/2P5/1P1PKPP1/Pk6/6NP/3N4/8 w - - 0 1
(White has 3 queens and 7 pawns, and White could only have one more queen than he has pawns promoted- he has two extra queens.)

There is no possible previous White move.
Sure there is. -1.Kf1 or -1.Kh1, then retract the check by bQ.
I only saw that after I posted it, whoops!
Changed the position.