You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.5 seconds
Memory limit: 256.0 MB

# Problem
You are given an $$$n \times n$$$ multiplication table and a positive integer $$$m = m_1 \cdot m_2$$$. A $$$n \times n$$$ multiplication table is a table with $$$n$$$ rows and $$$n$$$ columns numbered from $$$1$$$ to $$$n$$$, where $$$a_{i, j} = i \cdot j$$$.

For each divisor $$$d$$$ of $$$m$$$, check: does $$$d$$$ occur in the table at least once, and if it does, what is the minimum row that contains $$$d$$$.

## Input Format
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10$$$) — the number of test cases.

The first and only line of each test case contains three integers $$$n$$$, $$$m_1$$$ and $$$m_2$$$ ($$$1 \le n \le 10^9$$$; $$$1 \le m_1, m_2 \le 10^9$$$) — the size of the multiplication table and the integer $$$m$$$ represented as $$$m_1 \cdot m_2$$$.

## Output Format
For each test case, let $$$d_1, d_2, \dots, d_k$$$ be all divisors of $$$m$$$ sorted in the increasing order. And let $$$a_1, a_2, \dots, a_k$$$ be an array of answers, where $$$a_i$$$ is equal to the minimum row index where divisor $$$d_i$$$ occurs, or $$$0$$$, if there is no such row.

Since array $$$a$$$ may be large, first, print an integer $$$s$$$ — the number of divisors of $$$m$$$ that are present in the $$$n \times n$$$ table. Next, print a single value $$$X = a_1 \oplus a_2 \oplus \dots \oplus a_k$$$, where $$$\oplus$$$ denotes the bitwise XOR operation.

## Examples
```input
3
3 72 1
10 10 15
6 1 210
```
```output
6 2
10 0
8 5
```

## Note
In the first test case, $$$m = 72 \cdot 1 = 72$$$ and has $$$12$$$ divisors $$$[1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]$$$. The $$$3 \times 3$$$ multiplication table looks like that:

123112322463369

For each divisor of $$$m$$$ that is present in the table, the position with minimum row index is marked. So the array of answers $$$a$$$ is equal to $$$[1, 1, 1, 2, 2, 0, 3, 0, 0, 0, 0, 0]$$$. There are only $$$6$$$ non-zero values, and xor of $$$a$$$ is equal to $$$2$$$.

In the second test case, $$$m = 10 \cdot 15 = 150$$$ and has $$$12$$$ divisors $$$[1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150]$$$. All divisors except $$$75$$$ and $$$150$$$ are present in the $$$10 \times 10$$$ table. Array $$$a$$$ $$$=$$$ $$$[1, 1, 1, 1, 1, 1, 3, 5, 3, 5, 0, 0]$$$. There are $$$10$$$ non-zero values, and xor of $$$a$$$ is equal to $$$0$$$.

In the third test case, $$$m = 1 \cdot 210 = 210$$$ and has $$$16$$$ divisors $$$[1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210]$$$. The $$$6 \times 6$$$ table with marked divisors is shown below:

1234561123456224681012336912151844812162024551015202530661218243036

Array $$$a$$$ $$$=$$$ $$$[1, 1, 1, 1, 1, 0, 2, 0, 3, 0, 5, 0, 0, 0, 0, 0]$$$. There are $$$8$$$ non-zero values, and xor of $$$a$$$ is equal to $$$5$$$.

Now solve the problem and return the code.