You are given an array $$$a$$$ consisting of $$$n$$$ non-negative integers. It is guaranteed that $$$a$$$ is sorted from small to large.

For each operation, we generate a new array $$$b_i=a_{i+1}-a_{i}$$$ for $$$1 \le i \lt n$$$. Then we sort $$$b$$$ from small to large, replace $$$a$$$ with $$$b$$$, and decrease $$$n$$$ by $$$1$$$.

After performing $$$n-1$$$ operations, $$$n$$$ becomes $$$1$$$. You need to output the only integer in array $$$a$$$ (that is to say, you need to output $$$a_1$$$).

Input

The input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1\le t\le 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains one integer $$$n$$$ ($$$2\le n\le 10^5$$$) — the length of the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1,a_2,\dots,a_n$$$ ($$$0\le a_1\le \ldots\le a_n \le 5\cdot 10^5$$$) — the array $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2.5\cdot 10^5$$$, and the sum of $$$a_n$$$ over all test cases does not exceed $$$5\cdot 10^5$$$.

Output

For each test case, output the answer on a new line.

Note

To simplify the notes, let $$$\operatorname{sort}(a)$$$ denote the array you get by sorting $$$a$$$ from small to large.

In the first test case, $$$a=[1,10,100]$$$ at first. After the first operation, $$$a=\operatorname{sort}([10-1,100-10])=[9,90]$$$. After the second operation, $$$a=\operatorname{sort}([90-9])=[81]$$$.

In the second test case, $$$a=[4,8,9,13]$$$ at first. After the first operation, $$$a=\operatorname{sort}([8-4,9-8,13-9])=[1,4,4]$$$. After the second operation, $$$a=\operatorname{sort}([4-1,4-4])=[0,3]$$$. After the last operation, $$$a=\operatorname{sort}([3-0])=[3]$$$.

Difference Array

Examples