A14009. Strange List

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.

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 $10^5$ .

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

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]$ .