Sakurako has prepared a task for you:

She gives you an array of $$$n$$$ integers and allows you to choose $$$i$$$ and $$$j$$$ such that $$$i \neq j$$$ and $$$a_i \ge a_j$$$, and then assign $$$a_i = a_i - a_j$$$ or $$$a_i = a_i + a_j$$$. You can perform this operation any number of times for any $$$i$$$ and $$$j$$$, as long as they satisfy the conditions.

Sakurako asks you what is the maximum possible value of $$$mex_k$$$$$$^{\text{∗}}$$$ of the array after any number of operations.

Input format:
The first line contains a single integer $$$t$$$ ($$$1\le t\le 10^4$$$)  — the number of test cases.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1\le n\le 2\cdot 10^5,1\le k\le 10^9$$$)  — the number of elements in the array and the value $$$k$$$ for $$$mex_k$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots,a_n$$$ ($$$1\le a_i\le 10^9$$$)  — the elements of the array.

It is guaranteed that the sum of $$$n$$$ across all test cases does not exceed $$$2\cdot 10^5$$$.
Output format:
For each test case, output the maximum $$$mex_k$$$ that can be achieved through the operations.
Example Input 0:
6
1 3
3
2 10
1 1
3 1
1 2 3
3 2
1 2 4
4 5
2 2 2 16
4 5
2 2 2 3

Example Output 0:
2
11
3
4
8
8



Example input:
6
1 3
3
2 10
1 1
3 1
1 2 3
3 2
1 2 4
4 5
2 2 2 16
4 5
2 2 2 3


Example output:
2
11
3
4
8
8