codeforces#P1406E. Deleting Numbers
Deleting Numbers
Description
This is an interactive problem.
There is an unknown integer $x$ ($1\le x\le n$). You want to find $x$.
At first, you have a set of integers $\{1, 2, \ldots, n\}$. You can perform the following operations no more than $10000$ times:
- A $a$: find how many numbers are multiples of $a$ in the current set.
- B $a$: find how many numbers are multiples of $a$ in this set, and then delete all multiples of $a$, but $x$ will never be deleted (even if it is a multiple of $a$). In this operation, $a$ must be greater than $1$.
- C $a$: it means that you know that $x=a$. This operation can be only performed once.
Remember that in the operation of type B $a>1$ must hold.
Write a program, that will find the value of $x$.
The first line contains one integer $n$ ($1\le n\le 10^5$). The remaining parts of the input will be given throughout the interaction process.
Interaction
In each round, your program needs to print a line containing one uppercase letter A, B or C and an integer $a$ ($1\le a\le n$ for operations A and C, $2\le a\le n$ for operation B). This line desribes operation you make.
If your operation has type C your program should terminate immediately.
Else your program should read one line containing a single integer, which is the answer to your operation.
After outputting each line, don't forget to flush the output. To do it use:
- fflush(stdout) in C/C++;
- System.out.flush() in Java;
- sys.stdout.flush() in Python;
- flush(output) in Pascal;
- See the documentation for other languages.
It is guaranteed, that the number $x$ is fixed and won't change during the interaction process.
Hacks:
To make a hack, use such input format:
The only line should contain two integers $n$, $x$ ($1 \leq x \leq n \leq 10^5$).
Input
The first line contains one integer $n$ ($1\le n\le 10^5$). The remaining parts of the input will be given throughout the interaction process.
Samples
10
2
4
0
B 4
A 2
A 8
C 4
Note
Note that to make the sample more clear, we added extra empty lines. You shouldn't print any extra empty lines during the interaction process.
In the first test $n=10$ and $x=4$.
Initially the set is: $\{1,2,3,4,5,6,7,8,9,10\}$.
In the first operation, you ask how many numbers are multiples of $4$ and delete them. The answer is $2$ because there are two numbers divisible by $4$: $\{4,8\}$. $8$ will be deleted but $4$ won't, because the number $x$ will never be deleted. Now the set is $\{1,2,3,4,5,6,7,9,10\}$.
In the second operation, you ask how many numbers are multiples of $2$. The answer is $4$ because there are four numbers divisible by $2$: $\{2,4,6,10\}$.
In the third operation, you ask how many numbers are multiples of $8$. The answer is $0$ because there isn't any number divisible by $8$ in the current set.
In the fourth operation, you know that $x=4$, which is the right answer.