You are given an array $A$ of size $N$

Find the minimum non negative number $X$ such that there exist an index $j$ and when you can replace $A_j$ by $A_j+X$, the sum of elements of array from index $1$ to $j$  and $j+1$ to  $N$ becomes equal, where $1 \le j \le N-1$. Assume array to be 1-indexed.

If there is no possible $X$ print $-1$ in separate line.

Input Format

The first line contains $T$, the number of test cases.
For each Test case :
The first line contains an integer $N$, size of the array.
The second line contains $N$ space-separated integers, the $i^{th}$ of which is $A_i$.

Input Constraints

$1 \le T \le 10^{ 5}$
$2 \le N \le 10^{5}$
$0 \le A_i \le 10^{6}$
Sum of N all over testcases doesn't not exceed $10^{6}$.

Output Format

For each test case, print the required answer in separate line.