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F1. GCD Master (easy version)
time limit per test
3 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

This is the easy version of the problem. The only difference between the two versions is the constraint on $$$m$$$. You can make hacks only if both versions of the problem are solved.

You are given an array $$$a$$$ of length $$$n$$$ and two integers $$$m$$$ and $$$k$$$. Each element in $$$a$$$ satisfies $$$1\le a_i \le m$$$.

In one operation, you choose two indices $$$i$$$ and $$$j$$$ such that $$$1 \le i < j \le |a|$$$, then append $$$\gcd(a_i,a_j)$$$ to the back of the array and delete $$$a_i$$$ and $$$a_j$$$ from the array. Note that the length of the array decreases by one after this operation.

Find the maximum possible sum of the array after performing exactly $$$k$$$ operations.

Input

The first line contains a single integer $$$t$$$ ($$$1\le t\le 10^5$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains three integers $$$n$$$, $$$m$$$ and $$$k$$$ ($$$2 \le n \le 10^6$$$; $$$1\le m \le 10^6$$$; $$$1 \le k \le n-1$$$).

The second line of each test case contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \le a_i \le m$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^6$$$ and the sum of $$$m$$$ over all test cases does not exceed $$$10^6$$$.

Output

For each test case, output the maximum possible sum of the array after performing $$$k$$$ operations optimally.

Example
Input
3
3 8 1
4 7 8
5 114 2
7 2 4 1 6
3 514 2
2 3 3
Output
11
14
1
Note

In the first test case, the best way is to choose $$$i=1$$$, $$$j=3$$$ in the first operation. The final sequence is $$$[7,4]$$$.