P8178 "EZEC-11" Sequence

Given a sequence $f$ that satisfies $f_n = a_n f_{n-1} + b_n \ (n \ge 1)$. Determine whether there exists a non-negative integer $f_0$ such that for all $1 \le i \le k$, $f_i$ is a multiple of the **prime** $p_i$.

**This problem contains multiple test cases.** The first line contains an integer $T$, indicating the number of test cases. For each test case: - The first line contains an integer $k$. - The second line contains $k$ integers $a_1, a_2, \dots, a_k$. - The third line contains $k$ integers $b_1, b_2, \dots, b_k$. - The fourth line contains $k$ integers $p_1, p_2, \dots, p_k$, and it is **guaranteed that $p$ is prime**.

For each test case: - Output one string per line. If there exists an $f_0$ that satisfies the conditions, output `Yes`; otherwise, output `No`.

**[Sample 1 Explanation]** For the first test case, one feasible solution is $f_0 = 1$. In this case, $f_1 = 3, f_2 = 5, f_3 = 7$. For the second test case, there is no $f_0$ that satisfies the conditions. **[Constraints and Notes]** **This problem uses bundled tests.** - Subtask 1 (10 points): $k = 1$. - Subtask 2 (20 points): $k \le 2$. - Subtask 3 (20 points): $k \le 5$, $p_i \le 20$. - Subtask 4 (50 points): no special constraints. For $100\%$ of the testdata: $1 \le T \le 10$, $1 \le k \le 10^3$, $0 \le a_i, b_i \le 10^9$, $2 \le p_i \le 10^9$, and **$p$ is prime**. Translated by ChatGPT 5