1471B · Strange List

Problem: You have given an array $a$ of length $n$ and an integer $x$ to a brand new robot. What the robot does is the following: it iterates over the elements of the array, let the current element be $q$. If $q$ is divisible by $x$, the robot adds $x$ copies of the integer $\frac{q}{x}$ to the end of the array, and moves on to the next element. Note that the newly added elements could be processed by the robot later. Otherwise, if $q$ is not divisible by $x$, the robot shuts down.

Please determine the sum of all values of the array at the end of the process.

Input Format: The first input line contains a single integer $t$ ($1 \leq t \leq 100$) — the number of test cases.

The first line of each test case contains two integers $n$ and $x$ ($1 \leq n \leq 10^5$, $2 \leq x \leq 10^9$) — the length of the array and the value which is used by the robot.

The next line contains integers $a_1$, $a_2$, ..., $a_n$ ($1 \leq a_i \leq 10^9$) — the initial values in the array.

It is guaranteed that the sum of values $n$ over all test cases does not exceed $10^5$.

Output Format: For each test case output one integer — the sum of all elements at the end of the process.

Note: In the first test case the array initially consists of a single element $[12]$, and $x=2$. After the robot processes the first element, the array becomes $[12, 6, 6]$. Then the robot processes the second element, and the array becomes $[12, 6, 6, 3, 3]$. After the robot processes the next element, the array becomes $[12, 6, 6, 3, 3, 3, 3]$, and then the robot shuts down, since it encounters an element that is not divisible by $x = 2$. The sum of the elements in the resulting array is equal to $36$.

In the second test case the array initially contains integers $[4, 6, 8, 2]$, and $x=2$. The resulting array in this case looks like $[4, 6, 8, 2, 2, 2, 3, 3, 4, 4, 1, 1, 1, 1, 1, 1]$.