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.

长度为 $k$ 的数组 $b$ 被称为好数组，当且仅当它的算术平均值等于 $1$。更准确地说，满足

$$\frac{b_1 + \cdots + b_k}{k}=1.$$

注意：值 $\frac{b_1+\cdots+b_k}{k}$ 不进行向上或向下取整。例如，数组 $[1,1,1,2]$ 的算术平均值为 $1.25$，不等于 $1$。

给定一个长度为 $n$ 的整数数组 $a$。每次操作中，你可以在数组末尾追加一个非负整数。问：使该数组变为好数组所需的最少操作次数是多少？

我们已证明：总存在有限次操作可达成目标。

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.

第一行包含一个整数 $t$（$1 \leq t \leq 1000$），表示测试用例的数量。随后是 $t$ 个测试用例。

每个测试用例的第一行包含一个整数 $n$（$1 \leq n \leq 50$），表示初始数组 $a$ 的长度。

每个测试用例的第二行包含 $n$ 个整数 $a_1,\ldots,a_n$（$-10^4\leq a_i \leq 10^4$），即数组的元素。

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 $1$.

对于每个测试用例，输出一个整数——你需要附加到数组中的非负整数的最小个数，使得数组的算术平均值恰好为 $1$。

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 $1$.

在第一个测试用例中，我们无需添加任何元素，因为数组的算术平均值已经是 $1$，因此答案为 $0$。

在第二个测试用例中，初始时算术平均值不等于 $1$，因此我们需要至少再添加一个数。若添加 $0$，则整个数组的算术平均值变为 $1$，因此答案为 $1$。

在第三个测试用例中，需要添加的最少元素个数为 $16$，因为只允许添加非负整数。

在第四个测试用例中，我们可以添加一个整数 $4$。此时算术平均值变为 $\frac{-2+4}{2}$，其值等于 $1$。