P13995 【MX-X19-T4】「FeOI Round 4.5」Supernova

[Supernova - Yūnosuke / Haruno / KAITO / MORE MORE JUMP!](https://www.bilibili.com/video/BV15i421v7qP) > もっと響かせて この未知に賭けて

Haruka gives you three non-negative integers $x, y, p$. You can perform the following two operations any number of times (including zero) in any order: 1. Let $x \gets (x + 1) \mathbin{\vert} p$. 2. Let $x \gets x \mathbin{\vert} (p + 1)$. Here, $\mathbin{\vert}$ denotes the bitwise OR operation, and $a \gets b$ means assigning the value of $b$ to $a$. Haruka wants to know whether it is possible to transform $x$ into $y$ through these operations. If possible, she also wants to know the minimum number of operations required. Please help her solve this problem.

**The input contains multiple test cases.** The first line contains an integer $T$, indicating the number of test cases. For each test case: - One line containing three non-negative integers $x, y, p$.

For each test case, output one line. If there is a solution, output a non-negative integer representing the minimum number of operations; otherwise, output `-1`.

**【Sample Explanation】** For the first test case, it can be proven that no sequence of operations exists. For the second test case, perform operation 2 once: $x$ changes as $2 \to 6$. For the third test case, perform operation 1 four times: $x$ changes as $2 \to 3 \to 5 \to 7 \to 9$. **【Data Range】** **This problem uses bundled testing.** | Subtask ID | $T \le$ | $x, y \le$ | Special Properties | Score | | :--: | :--: | :--: | :--: | :--: | | $1$ | $5$ | $10$ | None | $9$ | | $2$ | $5$ | $10^7$ | None | $17$ | | $3$ | $10^4$ | $10^{18}$ | A | $22$ | | $4$ | $10^4$ | $10^{18}$ | B | $5$ | | $5$ | $10^4$ | $10^{18}$ | C | $14$ | | $6$ | $10^4$ | $10^{18}$ | None | $33$ | - Special Property A: If a solution exists, there is an optimal solution that uses only operation 1. - Special Property B: If a solution exists, there is an optimal solution that uses only operation 2. - Special Property C: $p = 1$. For all test cases, $1 \le T \le 10^4$, $0 \le x, y, p \le 10^{18}$. *Translated by DeepSeek V3.1*