In an under-construction village, $$$n$$$ houses have been built in a row numbered from $$$1$$$ to $$$n$$$. House $$$i$$$ has hospitality $$$h_i$$$.

The village has $$$n - 1$$$ roads, where road $$$i$$$ connects houses $$$i$$$ and $$$i + 1$$$ and will be built on day $$$d_i$$$. Initially, no roads are built.

You start at house $$$x$$$ and will stay in the village from day $$$1$$$ to day $$$k$$$, initially with a satisfaction of $$$0$$$. On day $$$s$$$, the following happens in order:

All roads $$$i$$$ with $$$d_i = s$$$ are built;
You may move to an adjacent house, if the road to it has been built, or stay at your current house;
Your satisfaction increases by $$$h_j$$$, where $$$j$$$ is the house you are currently at.

Find the maximum satisfaction you can achieve after $$$k$$$ days.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains three integers $$$n$$$, $$$k$$$ and $$$x$$$ ($$$2 \le n \le 2 \cdot 10^5$$$, $$$1 \le k \le 10^9$$$, $$$1 \le x \le n$$$) — the number of houses, the number of days and the starting house, respectively.

The second line contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$0 \le h_i \le 10^9$$$) — the hospitality of each house.

The third line contains $$$n - 1$$$ integers $$$d_1, d_2, \ldots, d_{n - 1}$$$ ($$$1 \le d_i \le k$$$) — the day each road is built.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output a single integer — the maximum satisfaction you can achieve after $$$k$$$ days.

Note

In the first test case, the following is one optimal sequence of moves:

You start at house $$$x = 3$$$ with a satisfaction of $$$0$$$.
On day $$$1$$$, no roads are built yet, so you must remain at house $$$3$$$. Your satisfaction becomes $$$3$$$.
On day $$$2$$$, road $$$3$$$ is built. You move to house $$$4$$$ and remain there on days $$$2$$$, $$$3$$$, $$$4$$$, $$$5$$$, $$$6$$$ and $$$7$$$. Your satisfaction becomes $$$33$$$. During this time, roads $$$2$$$ and $$$4$$$ are also built.
On day $$$8$$$, you move back to house $$$3$$$. Your satisfaction becomes $$$36$$$.
On day $$$9$$$, you move to house $$$2$$$. Your satisfaction becomes $$$38$$$.
On day $$$10$$$, road $$$1$$$ is built. You move to house $$$1$$$. Your satisfaction becomes $$$52$$$.

It can be shown that it is impossible to achieve a satisfaction greater than $$$52$$$.

In the second test case, you cannot reach house $$$4$$$ within $$$8$$$ days, so the maximum achievable satisfaction is $$$0$$$.

In the third test case, you can immediately move to house $$$2$$$ and remain there for $$$1\,000\,000\,000$$$ days.

Roadworks

Examples