P10252 Linear Transformation

You are given three non-negative integers $x, a, b$. As long as $x \ge 0$, you may perform the following operation on $x$ any number of times (including $0$ times): - Change $x$ to $ax - b$. You need to find the minimum value of $x$ that you can obtain through these operations.

**This problem contains multiple test cases.** The first line contains an integer $T$, the number of test cases. For each test case, one line contains three integers $x, a, b$.

For each test case, output one integer per line, the answer.

Sample explanation: For the first test case, $x = 6 \rightarrow 8 \rightarrow 12 \rightarrow \cdots$. Obviously, $x = 6$ is the minimum value. For the second test case, $x = 5 \rightarrow -1$, and $x = -1$ is the minimum value. ---- Constraints: For $30\%$ of the testdata, $T \le 5$, and $x, a, b \le 100$. For another $20\%$ of the testdata, $a > b$. For another $20\%$ of the testdata, $b = 0$. For $100\%$ of the testdata, $1 \le T \le 1000$, and $0 \le x, a, b \le 10^{9}$. Translated by ChatGPT 5