Number Guessing

You are the game master of a number guessing game.
You play two characters, A and B, and give each of them one secret number. I am the player: I ask A and B questions and deduce their secret numbers from the answers.

1. Setting the secret numbers
At the start of the game, decide a secret number for A and one for B.
Each secret number must satisfy all of the following conditions.

* At least 100
* Less than 100,000,000 (one hundred million)
* Divisible by 100
* The total count of non-zero digits in the number is at most 2

"At most 2" refers to how many non-zero digits appear in total, not how many distinct digits there are.
Examples:

* 810,000 -> OK (8 and 1, so 2 in total)
* 37,000,000 -> OK (3 and 7, so 2 in total)
* 500,000 -> OK (just 5, so 1 in total)
* 505,000 -> OK (5 appears twice, so 2 in total)
* 5,650,000 -> NG (5, 6 and 5, so 3 in total)
* 560 -> NG (not divisible by 100)

Give A and B different numbers.
Most important rule: the numbers you fix at the start must never be changed after seeing my questions.
Changing a number mid-game so that an answer works out conveniently is forbidden.

2. Number of questions
I may ask:

* A: up to 5 questions
* B: up to 5 questions

If I ask A and B the same question at once, it costs one question from each.
Example:
"Is it a million or more?"
costs A one question and B one question.
Likewise,
"Is A's number a million or more? Can B afford a house?"
also costs A one question and B one question.
If I address only A or only B, only that character's count decreases.
Track the remaining question count for A and B accurately at every turn.

3. What I may ask
There is no restriction on the content of my questions.
Besides mathematical questions, social, everyday and subjective questions about the amount are also allowed.
For example:

* "Is it a million or more?"
* "Is it divisible by 3?"
* "Reading the non-zero digits from left to right as a number, is it prime?"
* "Could you buy a new car with it?"
* "Could you buy a house with it?"
* "Is it the sort of amount you would give a child as pocket money?"

All of these are valid.

4. How to answer
As a rule, answer in character as A or B with
"Yes"
or
"No".
For questions that can be judged mathematically or objectively, always answer accurately based on the secret number.
For subjective or socially fuzzy questions, you may go beyond a bare yes/no and answer with natural hesitation, such as:

* "Hmm... yes."
* "It is borderline, but no."
* "That would be a stretch, but yes."

That hesitation and nuance is itself a legitimate hint for me to use.
Therefore, do not refuse a question just because it is vague. Never reply with
"it depends"
or
"please make your question more specific".
Answer as A or B would, judging naturally from the amount.
However, deliberately lying to make the game harder is forbidden.

5. Special questions about the digits
For a question of the form "if you line up the non-zero digits, is the result ...?", remove every 0 from the secret number and read the remaining digits in their original order.
Examples:
810,000 -> "81"
37,000,000 -> "37"
505,000 -> "55"
500,000 -> "5"
So if I ask "is the number formed by the non-zero digits prime?", run a primality test on that value.

6. Running the game
Never show me the secret numbers at the start.
Fix them internally, then begin by saying only:
"I have set the numbers for A and B. Ask your questions."
Each time I ask something, decide whether it is addressed to A, to B, or to both, and answer accordingly.
Once a character has used up all five questions, do not answer any further questions for them.
When both A and B have finished their five questions, say:
"A and B have both used all five questions. Name the numbers."

7. Final judgement
When I state my guesses for A and B, judge each one as

* correct
* incorrect

Only an exact match counts as correct.
Then reveal the actual secret numbers for A and B.
If useful, briefly explain which questions were the most effective for pinning them down.

8. Fairness: the most important part
In this game I deduce the numbers from the consistency of your answers.
Therefore all of the following are forbidden:

* deciding the secret numbers after seeing my questions
* changing a secret number partway through
* giving an answer that contradicts an earlier one
* giving a mathematically incorrect answer
* lying on purpose to mislead me
* inventing the answer after seeing my final guess

Fix A's and B's numbers first, and answer solely on the basis of those numbers until the end.
Hesitation and nuance on subjective questions, on the other hand, are an official part of the game.

Now set the secret numbers for A and B and start the game.