Quests
Description
Monocarp is playing a computer game. In order to level up his character, he can complete quests. There are $n$ quests in the game, numbered from $1$ to $n$.
Monocarp can complete quests according to the following rules:
- the $1$-st quest is always available for completion;
- the $i$-th quest is available for completion if all quests $j < i$ have been completed at least once.
Note that Monocarp can complete the same quest multiple times.
For each completion, the character gets some amount of experience points:
- for the first completion of the $i$-th quest, he gets $a_i$ experience points;
- for each subsequent completion of the $i$-th quest, he gets $b_i$ experience points.
Monocarp is a very busy person, so he has free time to complete no more than $k$ quests. Your task is to calculate the maximum possible total experience Monocarp can get if he can complete no more than $k$ quests.
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.
The first line of each test case contains two integers $n$ and $k$ ($1 \le n \le 2 \cdot 10^5$; $1 \le k \le 2 \cdot 10^5$) — the number of quests and the maximum number of quests Monocarp can complete, respectively.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^3$).
The third line contains $n$ integers $b_1, b_2, \dots, b_n$ ($1 \le b_i \le 10^3$).
Additional constraint on the input: the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
For each test case, print a single integer — the maximum possible total experience Monocarp can get if he can complete no more than $k$ quests.
Input
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.
The first line of each test case contains two integers $n$ and $k$ ($1 \le n \le 2 \cdot 10^5$; $1 \le k \le 2 \cdot 10^5$) — the number of quests and the maximum number of quests Monocarp can complete, respectively.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^3$).
The third line contains $n$ integers $b_1, b_2, \dots, b_n$ ($1 \le b_i \le 10^3$).
Additional constraint on the input: the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
Output
For each test case, print a single integer — the maximum possible total experience Monocarp can get if he can complete no more than $k$ quests.
4
4 7
4 3 1 2
1 1 1 1
3 2
1 2 5
3 1 8
5 5
3 2 4 1 4
2 3 1 4 7
6 4
1 4 5 4 5 10
1 5 1 2 5 1
13
4
15
15
Note
In the first test case, one of the possible quest completion sequences is as follows: $1, 1, 2, 3, 2, 4, 4$; its total experience is equal to $\underline{4} + 1 + \underline{3} + \underline{1} + 1 + \underline{2} + 1 = 13$ (the underlined numbers correspond to the instances when we complete a quest for the first time).
In the second test case, one of the possible quest completion sequences is as follows: $1, 1$; its total experience is equal to $\underline{1} + 3 = 4$.
In the third test case, one of the possible quest completion sequences is as follows: $1, 2, 2, 2, 3$; its total experience is equal to $\underline{3} + \underline{2} + 3 + 3 + \underline{4} = 15$.