A16212 | Helmets in Night Light

Pak 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?

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 $10^5$ .

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