P9703 "TFOI R1" Average Number

**The background is unrelated to the problem and can be skipped; you may read the description directly.** There is a kind of person called "someone else’s little sister", and Little A deeply relates to this. Little A’s younger sister—Little L—often steals Little A’s stored books to read, which gives Little A a real headache. This time, perfectionist Little A was tidying up his book collection, and Little L took one book while he was not paying attention. "Give it back to me." "No. But... if you can guess the ID number of the book in my hand, I will give it back to you." To make it easier to take and organize his collection, Little A numbered every book starting from $1$. "You must be joking. I have so many books—how can I guess?" "Okay. Then I will tell you the average of the ID numbers of the remaining pile of books. How about that? Is this hint enough?" "..." Little A has so many books that he does not even know how many there are. But as a qualified OIer, with the help of a computer, Little A successfully computed the answer. However, he wants to use this problem to test you.

You are given the value of $\dfrac{\left(\sum\limits^{n}_ {i = 1}i \right) - m}{n - 1}$, where $m \in [1, n]$, and both $n$ and $m$ are positive integers. You need to determine the values of $n$ and $m$. A solution is guaranteed to exist. If there are multiple feasible solutions, output the one with the smaller $n$. Multiple test cases.

The first line contains a positive integer $T$, the number of test cases. The next $T$ lines each contain three non-negative integers $a, b, c$, meaning the average value is $a + \dfrac{b}{c}$.

Output $T$ lines. Each line contains two positive integers, representing $n$ and $m$.

**This problem uses bundled tests.** - Subtask 1 (5 points): $T \leqslant 10$, $n \leqslant 10^3$. - Subtask 2 (5 points): $T \leqslant 10^3$, $n \leqslant 10^3$. - Subtask 3 (5 points): $T \leqslant 10$, $n \leqslant 5\times 10^5$. - Subtask 4 (40 points): $T \leqslant 10^3$, $n \leqslant 10^{18}$. - Subtask 5 (45 points): No special constraints. For all testdata, $1 \leqslant m \leqslant n \leqslant 10 ^ {18}$, $n \not = 1$, $1 \leqslant T \leqslant 2 \times 10 ^{5}$, $1 \leqslant a \leqslant 10 ^{18}$, $0 \leqslant b < c \leqslant 10 ^ {18}$. **It is guaranteed that $\dfrac{b}{c}$ is a reduced proper fraction. In particular, when $b=0$, $c=1$.** --- **Background (continued)** "Y-you... how did you guess it?" As Little L spoke, the surprise in her eyes at Little A gained an extra bit of admiration. "Hah, how could a problem of this difficulty possibly stump me?" "Ah. If that is the case, then let’s play one more time!" "..." Translated by ChatGPT 5