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C. Quiz Master

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA school has to decide on its team for an international quiz. There are $$$n$$$ students in the school. We can describe the students using an array $$$a$$$ where $$$a_i$$$ is the smartness of the $$$i$$$-th ($$$1 \le i \le n$$$) student.

There are $$$m$$$ topics $$$1, 2, 3, \ldots, m$$$ from which the quiz questions will be formed. The $$$i$$$-th student is considered proficient in a topic $$$T$$$ if $$$(a_i \bmod T) = 0$$$. Otherwise, he is a rookie in that topic.

We say that a team of students is collectively proficient in all the topics if for every topic there is a member of the team proficient in this topic.

Find a team that is collectively proficient in all the topics such that the maximum difference between the smartness of any two students in that team is minimized. Output this difference.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains $$$n$$$ and $$$m$$$ ($$$1 \le n,m \le 10^5$$$).

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^5$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

It is guaranteed that the sum of $$$m$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case, print the answer on a new line. If there is no solution, output $$$-1$$$.

Example

Input

32 43 74 23 7 2 95 76 4 3 5 7

Output

-1 0 3

Note

In the first test case, we have participants with smartnesses $$$3$$$ and $$$7$$$, and $$$m = 4$$$. Thus, there is no student with smartness divisible by $$$2$$$. Since $$$2 \leq m$$$, there is no way to choose a team.

In the second test case, we can select the participant with smartness $$$2$$$ to be the only one on the team. This way the team will be collectively proficient in both topics $$$1$$$ and $$$2$$$.

In the third test case, consider the team with participants of smartnesses $$$4, 5, 6, 7$$$. This way the team will be collectively proficient in all topics $$$1, 2, \ldots, 7$$$.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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