1471_B. 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 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

The first input line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases.

The first line of each test case contains two integers n and x (1 ≤ n ≤ 10^5, 2 ≤ x ≤ 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 ≤ a_i ≤ 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

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

Example

Input


2
1 2
12
4 2
4 6 8 2


Output


36
44

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].
```python
t=int(input())
for _ in range(t):
    n,x=[int(z) for z in input().split()]
    a=[int(x) for x in input().split()]
    
    minCycles=float('inf')
    minCycIdx=-1
    for i,z in enumerate(a):
        nCycles=0
        while z%x==0:
            nCycles+=1
            z//=x
        if nCycles<minCycles:
            minCycles=nCycles
            minCycIdx=i
    
    ans=0
    for i,z in enumerate(a):
        if i<minCycIdx:
            minCycles2=minCycles+1 #can have 1 more cycle since it comes before the min cyc index
        else:
            minCycles2=minCycles
        ans+=z
        cycCnt=0
        z2=z
        while z2%x==0 and cycCnt<minCycles2:
            ans+=z
            z2//=x
            cycCnt+=1
    print(ans)
```