#P1537A. Arithmetic Array
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ID: 5965
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Arithmetic Array
No submission language available for this problem.
Description
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 $1$.
Input
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.
Output
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 $1$.
Samples
4
3
1 1 1
2
1 2
4
8 4 6 2
1
-2
0
1
16
1
Note
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 $1$.