[pilun]

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East got to show 4-5-3-1.
3NT showed 7 SPs (QPs)
We count stiff kings as 1 SP (David Morgan's recommendation)
In our simple DCB, stop = 0 or 4+ SP (so none or AQ/AK(Q))
We switch to positive with singletons, so
4NT = H-y, S-y, D-y, C-y

so has to be the actual.
♦Q not needed so this time kontrol ask would work nicely as well.
(On the other hand, West might want to avoid 6♥ opposite xxxx, KJxxx, KQx, K)

A bit tougher in methods that ignore stiff kings, like KK relay.

[foobar]

awm doesn't discount stiffs, so wonder how KK-relay might do here with that option.

After 3!D - 3!H asks:

4C (4 controls) - 4D - 4H (DCB) - 5C (heart, spade, not QH). Note that the scan skips the second shortest suit. In this case, there's some ambiguity about KD or KC, but either should do on this hand.

[awm]

Easy for Sam and me of course:

1♥ - 1NT (GF relay or good invite with 5+♠)
2♥ (4♠) - 2♠ (GF relay)
3♦ (4531) - 3♥ (RP?)
4♣ (8) - 4♦ (relay)
4♥ (singleton honor in clubs) - 4♠ (relay)
5♥ (one top honor in each suit; K in hearts and Q in diamonds rather than vice-versa)

At this point responder knows all the cards, so 7♥ is clear.