#P1641A. Great Sequence
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ID: 6304
Type: RemoteJudge
1000ms
256MiB
Tried: 1
Accepted: 0
Difficulty: 10
Uploaded By:
Hydro
Tags> Great Sequence
No submission language available for this problem.
Description
A sequence of positive integers is called great for a positive integer $x$, if we can split it into pairs in such a way that in each pair the first number multiplied by $x$ is equal to the second number. More formally, a sequence $a$ of size $n$ is great for a positive integer $x$, if $n$ is even and there exists a permutation $p$ of size $n$, such that for each $i$ ($1 \le i \le \frac{n}{2}$) $a_{p_{2i-1}} \cdot x = a_{p_{2i}}$.
Sam has a sequence $a$ and a positive integer $x$. Help him to make the sequence great: find the minimum possible number of positive integers that should be added to the sequence $a$ to make it great for the number $x$.
Each test contains multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 20\,000$) — the number of test cases. Description of the test cases follows.
The first line of each test case contains two integers $n$, $x$ ($1 \le n \le 2 \cdot 10^5$, $2 \le x \le 10^6$).
The next line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
For each test case print a single integer — the minimum number of integers that can be added to the end of $a$ to make it a great sequence for the number $x$.
Input
Each test contains multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 20\,000$) — the number of test cases. Description of the test cases follows.
The first line of each test case contains two integers $n$, $x$ ($1 \le n \le 2 \cdot 10^5$, $2 \le x \le 10^6$).
The next line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
Output
For each test case print a single integer — the minimum number of integers that can be added to the end of $a$ to make it a great sequence for the number $x$.
Samples
4
4 4
1 16 4 4
6 2
1 2 2 2 4 7
5 3
5 2 3 5 15
9 10
10 10 10 20 1 100 200 2000 3
0
2
3
3
Note
In the first test case, Sam got lucky and the sequence is already great for the number $4$ because you can divide it into such pairs: $(1, 4)$, $(4, 16)$. Thus we can add $0$ numbers.
In the second test case, you can add numbers $1$ and $14$ to the sequence, then you can divide all $8$ integers into such pairs: $(1, 2)$, $(1, 2)$, $(2, 4)$, $(7, 14)$. It is impossible to add less than $2$ integers to fix the sequence.