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A. Helmets in Night Light

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPak Chanek is the chief of a village named Khuntien. On one night filled with lights, Pak Chanek has a sudden and important announcement that needs to be notified to all of the $$$n$$$ residents in Khuntien.

First, Pak Chanek shares the announcement directly to one or more residents with a cost of $$$p$$$ for each person. After that, the residents can share the announcement to other residents using a magical helmet-shaped device. However, there is a cost for using the helmet-shaped device. For each $$$i$$$, if the $$$i$$$-th resident has got the announcement at least once (either directly from Pak Chanek or from another resident), he/she can share the announcement to at most $$$a_i$$$ other residents with a cost of $$$b_i$$$ for each share.

If Pak Chanek can also control how the residents share the announcement to other residents, what is the minimum cost for Pak Chanek to notify all $$$n$$$ residents of Khuntien about the announcement?

Input

Each test contains multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases. The following lines contain the description of each test case.

The first line contains two integers $$$n$$$ and $$$p$$$ ($$$1 \leq n \leq 10^5$$$; $$$1 \leq p \leq 10^5$$$) — the number of residents and the cost for Pak Chanek to share the announcement directly to one resident.

The second line contains $$$n$$$ integers $$$a_1,a_2,a_3,\ldots,a_n$$$ ($$$1\leq a_i\leq10^5$$$) — the maximum number of residents that each resident can share the announcement to.

The third line contains $$$n$$$ integers $$$b_1,b_2,b_3,\ldots,b_n$$$ ($$$1\leq b_i\leq10^5$$$) — the cost for each resident to share the announcement to one other resident.

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

Output

For each test case, output a line containing an integer representing the minimum cost to notify all $$$n$$$ residents of Khuntien about the announcement.

Example

Input

36 32 3 2 1 1 34 3 2 6 3 61 10000010000014 941 4 2 3103 96 86 57

Output

16 100000 265

Note

In the first test case, the following is a possible optimal strategy:

- Pak Chanek shares the announcement directly to the $$$3$$$-rd, $$$5$$$-th, and $$$6$$$-th resident. This requires a cost of $$$p+p+p=3+3+3=9$$$.
- The $$$3$$$-rd resident shares the announcement to the $$$1$$$-st and $$$2$$$-nd resident. This requires a cost of $$$b_3+b_3=2+2=4$$$.
- The $$$2$$$-nd resident shares the announcement to the $$$4$$$-th resident. This requires a cost of $$$b_2=3$$$.

The total cost is $$$9+4+3=16$$$. It can be shown that there is no other strategy with a smaller cost.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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