[Solution] Far Away CodeChef Solution | Solution CodeChef

Problem

Chef has an array $A$ of size $N$ and an integer $M$, such that $1 \leq A_i \leq M$ for every $1 \leq i \leq N$.

The distance of an array $B$ from array $A$ is defined as:

$$d(A, B) = \sum_{i=1}^N |A_i - B_i|$$

Chef wants an array $B$ of size $N$, such that $1 \le B_i \le M$ and the value $d(A, B)$ is as large as possible, i.e, the distance of $B$ from $A$ is maximum.

Find the maximum distance for any valid array $B$.

Note: $|X|$ denotes the absolute value of an integer $X$. For example, $|-4| = 4$ and $|7| = 7$.

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• Each test case consists of two lines of input.
  • The first line of each test case contains two space-separated integers $N$ and $M$ — the length of array $A$ and the limit on the elements of $A$ and $B$.
  • The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

Output Format

For each test case, output on a new line the maximum distance of an array from $A$.

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Explanation:

Test case $1$: The array having maximum distance from $A$ is $B = [6, 1]$. Thus the distance is $|3-6| + |5-1| = 3+4=7$.

Test case $2$: The only array possible is $B = [1,1,1,1]$. The distance of this array from $A$ is $0$.

Test case $3$: One of the possible arrays having maximum distance from $A$ is $B = [7,7,1,1,1]$. Thus the distance is $|2-7| + |3-7| + |4-1| + |5-1| + |6-1| = 5+4+3+4+5=21$.