Impossible defense

I don't want to fill the world with sob stories but this is really a good one. Defense is hard enough when you've got all the information. When you don't it's harder but when the opponents have outright lied harder still.

Imagine you're south, listen carefully to the bidding:

North	East	South	West
-	2♥1	Pass	4NT2
Pass	5♦3	Pass	5♥4
Pass	6♥5	Pass	Pass
Pass

If you're short of time I'll help you out:

1. 5♥ & 4+ minor, weak
2. Months out of tempo. Keycard Blackwood.
3. 1 or 4 keycards
4. Sign off
5. ???

You stare down meaningfully at your hand and find a suitable lead like the K♠.

♠ Q J 3 ♥ K Q 9 7 6 2 ♦ A Q 8 ♣ K
	♠ A K T 6 ♥ 8 5 ♦ J T 5 3 2 ♣ J 7

Partner is a diligent soul and plays the 9♠ declarer plays the 5♠. That's reverse count and shows and odd number meaning declarer has 1 or 3 spades.

Lets summarize what we know. Partner doesn't have any hearts so declarer has the Ace and Jack. Declarer has no spade cards so either the Ace of clubs or the King of diamonds. What's the defense on these possible layouts?

♠ 7 5 2 ♥ A J T 4 3 ♦ - ♣ A T 9 8 5

♠ 7 5 2 ♥ A J T 4 3 ♦ K ♣ A 8 5 4

♠ 5 ♥ A J T 4 3 ♦ 7 4 ♣ A 9 8 5 4

Hand 1 it doesn't matter a bean; this contract is doomed. Hand 2; cash the spade, or they have the rest of the tricks. Hand 3 you switch, to anything, take your hand off that spade and no one gets hurt.

You can guess which hand was at the table. Couldn't even rely on something simple like: open 12 counts at the 1 level. Next board please.