EW end up in 1NT while 3NT would have been a very good contract.

♠	A 9 6 5			♠	K Q 3
♥	8 6 5			♥	A J 7
♦	9 7			♦	K Q 10 8
♣	Q 10 7 5			♣	A 9 8

'I thought you showed 13-14 HCP', West says.
'I wouldn't double with so little points if I have an unsuitable distribution for it. After all, my second bid shows that I have some length in diamonds', East says.
'Not necessarily, since you could have something like ♦Ax, a guard and still a short diamond suit', West says.

Who is wrong and who is right?

Solution

West was wrong. East's bidding shows a balanced hand with 18-19 HCP — a hand therefore, too strong to overcall 1NT directly. It is quite logical that East is strong, since West may have bid 1♠ on zero points (the bid shows 0-7). Bidding 1NT on a mere 13-14 count would be close to suicidal.
Note the structural difference between overcalling directly and doubling first, followed by that bid. We use the second sequence (first double, than the bid) to show a hand that is too strong to make that overcall directly.
Some examples:

South shows at least five spades and 18 HCP or more. His hand does not have to meet the usual demands for a take-out double on 1♣ (which are, in case of a minimum double: at most two clubs, at least three cards in the other suits, at least 4-3 or 3-4 in the majors).
He says: 'I have the distribution for a 1♠ overcall, but was too strong for that bid.'

South shows 18-19 HCP and a balanced hand. He was too strong for a direct 1NT overcall.

South shows a hand too strong for a direct 2♠ jump overcall. So if that direct overcall were to show 12-16 HCP (intermediate jump overcall), the sequence via the double shows 17⁺ HCP.

Now let's return to our problem:

¹ Wrong, as we have seen by now, since 1NT shows 18-19 HCP

West said: '...you could have something like ♦Ax, a guard and still a short diamond suit'. West means a hand like:

♠	A 9 6 5			♠	Q 3 2
♥	8 6 5			♥	A J 7 4
♦	9 7			♦	A 4
♣	Q 10 7 5			♣	K 9 8 2

West suggests that this is a hand with which East would double first and bid 1NT later. West is wrong, we know that now: this kind of bidding would be near suicidal since West could have bid 1♠ on zero points.
The question remains what East should bid then over West's 1♠ bid. The answer is: PASS! He has doubled for take-out, showing opening strength. West reacts by bidding a suit without jumping. This means that he thinks that this is the right contract! So East will only bid on with (a lot of) extra strength. West's 1♠ bid is not forcing. It shows as we have seen 0-7 HCP.

Quite different therefore from the situation after an opening bid by East and a 1♠ response by West: that 1♠ bid shows 6 HCP or more: it is forcing, since it is unlimited.
Experience shows that beginning players tend to mix up both situations! Therefore once again, this time in diagrams:

North shows 0-7 HCP. His bid is not forcing.
If South makes another bid he shows a very strong hand:
1NT: 18-19
2♦/♥: about the same
2♠: a bit less in HCP. Since there is a fit, South can add distributional points. But still 2♠ shows a strong hand!
With a minimum hand or with only little extra strength, South should pass!

North shows 0-7 HCP. His bid is forcing.
South's 1NT rebid now shows 13-14 HCP.

Keep in mind: after partner's opening, the bidding is totally different from after his take-out double.