CF1777C.Quiz Master

A 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.

一所学校需要为其参加国际知识竞赛的队伍做出选择。学校共有 $n$ 名学生。我们可以用一个数组 $a$ 来描述这些学生，其中 $a_i$ 表示第 $i$ 名学生（$1 \le i \le n$）的“聪慧值”。

竞赛题目将从 $m$ 个主题 $1, 2, 3, \ldots, m$ 中选取。若第 $i$ 名学生满足 $(a_i \bmod T) = 0$，则称其在主题 $T$ 上是“熟练的”；否则，称其在该主题上为“新手”。

若一支学生队伍对所有主题均“集体熟练”，即：对每个主题 $T$（$1 \le T \le m$），该队伍中至少有一名学生在主题 $T$ 上是熟练的。

请找出一支对所有主题均集体熟练的学生队伍，使得该队伍中任意两名学生聪慧值之差的最大值最小化。输出该最小化的最大差值。

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 $10^5$.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 10^4$）。随后是各测试用例的描述。

每个测试用例的第一行包含两个整数 $n$ 和 $m$（$1 \le n,m \le 10^5$）。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$1 \le a_i \le 10^5$）。

保证所有测试用例的 $n$ 之和不超过 $10^5$。

保证所有测试用例的 $m$ 之和不超过 $10^5$。

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

对于每个测试用例，在新的一行输出答案。若无解，输出 $-1$。

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 $1, 2, \ldots, 7$.

在第一个测试用例中，我们有聪明度分别为 $3$ 和 $7$ 的参与者，且 $m = 4$。因此，不存在聪明度能被 $2$ 整除的学生。由于 $2 \leq m$，故无法组成队伍。

在第二个测试用例中，我们可以仅选择聪明度为 $2$ 的参与者组成队伍。这样，该队伍将共同精通主题 $1$ 和 $2$。

在第三个测试用例中，考虑由聪明度分别为 $4, 5, 6, 7$ 的参与者组成的队伍。这样，该队伍将共同精通所有主题 $1, 2, \ldots, 7$。