A14292 | Arithmetic Array

An array $b$ of length $k$ is called good if its arithmetic mean is equal to $1$ . More formally, if $$$$\frac{b_1 + \cdots + b_k}{k}=1. $$ </p><p>Note that the value $\\frac{b\_1+\\cdots+b\_k}{k}$ is not rounded up or down. For example, the array $\[1,1,1,2\]$ has an arithmetic mean of $1.25$ , which is not equal to $1$ .</p><p>You are given an integer array $a$ of length $n$$$. In an operation, you can append a non-negative integer to the end of the array. What's the minimum number of operations required to make the array good?

We have a proof that it is always possible with finitely many operations.

The first line contains a single integer $t$ ( $1 \leq t \leq 1000$ ) — the number of test cases. Then $t$ test cases follow.

The first line of each test case contains a single integer $n$ ( $1 \leq n \leq 50$ ) — the length of the initial array $a$ .

The second line of each test case contains $n$ integers $a_1,\ldots,a_n$ ( $-10^4\leq a_i \leq 10^4$ ), the elements of the array.

For each test case, output a single integer — the minimum number of non-negative integers you have to append to the array so that the arithmetic mean of the array will be exactly $1$ .