CF1537A.Arithmetic Array

An array $b$ of length $k$ is called good if its arithmetic mean is equal to $1$ . More formally, if $$$$\frac{b_1 + \cdots + b_k}{k}=1. $$

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 $1$ .

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 $1$ .

In the first test case, we don't need to add any element because the arithmetic mean of the array is already $1$ , so the answer is $0$ .

In the second test case, the arithmetic mean is not $1$ initially so we need to add at least one more number. If we add $0$ then the arithmetic mean of the whole array becomes $1$ , so the answer is $1$ .

In the third test case, the minimum number of elements that need to be added is $16$ since only non-negative integers can be added.

In the fourth test case, we can add a single integer $4$ . The arithmetic mean becomes $\frac{-2+4}{2}$ which is equal to $1$ .