CF1914C.Quests

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题目描述

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.

输入格式

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 $2 \cdot 10^5$ .

输出格式

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.

输入输出样例

输入#1

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

输出#1

说明/提示

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

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