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 $ .