[Solution] Difference Array Solution Codeforces | Codeforces Solution

D. Difference Array

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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

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

After performing n−1$n-1$ operations, n$n$ becomes 1$1$. You need to output the only integer in array a$a$ (that is to say, you need to output a1$a_1$).

Input

The input consists of multiple test cases. The first line contains a single integer t$t$ (1≤t≤104$1\le t\le {10}^4$) — the number of test cases. The description of the test cases follows.

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The first line of each test case contains one integer n$n$ (2≤n≤105$2\le n\le {10}^5$) — the length of the array a$a$.

The second line contains n$n$ integers a1,a2,…,an$a_1,a_2,\dots ,a_n$ (0≤a1≤…≤an≤5⋅105$0\le a_1\le \dots \le a_n\le 5\cdot {10}^5$) — the array a$a$.

It is guaranteed that the sum of n$n$ over all test cases does not exceed 2.5⋅105$2.5\cdot {10}^5$, and the sum of an$a_n$ over all

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 test cases does not exceed 5⋅105$5\cdot {10}^5$.

Output

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