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 $$$j \lt i$$$ 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.

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.

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 $$$\underline{3} + \underline{2} + 3 + 3 + \underline{4} = 15$$$.

Quests

Examples