Find Missing Number in Arithmetic Progression

You are given an array that represents an arithmetic progression with exactly one missing element. The full arithmetic progression should contain n numbers, but the provided array contains only n - 1 numbers. Use the formula for the sum of an arithmetic progression: $$S = \frac{n(a_1 + a_n)}{2}$$ to determine the missing number.

For example, given the array [2, 4, 8, 10], the missing number is 6.

inputFormat

The first line contains an integer T denoting the number of test cases. Each test case starts with an integer k representing the number of given elements, followed by k space-separated integers which form the arithmetic progression with one missing element.

outputFormat

For each test case, output the missing number on a separate line.

5
4 2 4 8 10
3 1 7 10
3 3 9 12
4 5 10 20 25
3 5 15 20

6
4
6
15
10