题目描述

As we all know, the number of $\textit{Pang}$'s papers follows exponential growth. Therefore, we are curious about $\textit{King}$ sequence.

You are given a prime $p$. A sequence $(a_1,a_2,\ldots,a_n)$ is a $\textit{King}$ sequence if and only if there is an integer $1\leq q < p$ such that for all integers $i\in [2,n]$, $q a_{i-1} \equiv a_i \pmod p$.

Given a sequence $B=(b_1,\ldots,b_m)$, what is the length of the longest $\textit{King}$ subsequence of $B$?

A subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

$Pang$ is super busy recently, so the only thing he wants to know is whether the answer is greater than or equal to $\frac{n}{2}$.

If the length of the longest $\textit{King}$ sequence is less than $\frac{n}{2}$, output $-1$. Otherwise, output the length of the longest $\textit{King}$ subsequence.

输入格式

The first line contains an integer $T$ denoting the number of test cases ($1\le T\le 1000$).

The first line in a test case contains two integers $n$ and $p$ ($2\le n \le 200000$, $2\le p \le 1000000007$, $p$ is a prime). The sum of $n$ over all test cases does not exceed $200000$.

The second line in a test case contains a sequence $b_1,\ldots, b_n$ ($1\le b_i< p$).

输出格式

For each test case, output one line containing the answer which is $-1$ or the length of the longest $\textit{King}$ subsequence.

4
6 1000000007
1 1 2 4 8 16
6 1000000007
597337906 816043578 617563954 668607211 89163513 464203601
5 1000000007
2 4 5 6 8
5 1000000007
2 4 5 6 7

5
-1
3
-1