CF2238A.Another Puzzle from Papyrus

You are filled with determination.

— Undertale

Papyrus came up with another puzzle for Frisk to solve. Papyrus brought two arrays $a$ and $b$ of length $n$ and allowed the following two operations to be performed:

• choose any index $i$ ($1 \le i \le n$) and change $a_i$ to $a_i - 1$. The execution time of such an operation is $1$ second.
• reorder all elements of array $a$ in any way. The execution time of such an operation is $c$ seconds.

You need to convert array $a$ into array $b$.

Frisk wants to solve the puzzle as soon as possible. Help Frisk determine the minimum time needed to solve the puzzle. If there is no solution, output $-1$.

你充满了决心。

——《Undertale》

帕派瑞斯（Papyrus）又为弗里斯克（Frisk）设计了一个谜题。帕派瑞斯带来了两个长度为 $n$ 的数组 $a$ 和 $b$，并允许执行以下两种操作：

• 选择任意下标 $i$（$1 \le i \le n$），将 $a_i$ 修改为 $a_i - 1$。该操作耗时 $1$ 秒。
• 以任意方式重排数组 $a$ 的所有元素。该操作耗时 $c$ 秒。

你需要将数组 $a$ 转换为数组 $b$。

弗里斯克希望尽快解出该谜题。请帮助弗里斯克确定解出谜题所需的最短时间。若无解，请输出 $-1$。

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 500$). The description of the test cases follows.

The first line of each test case contains two integers $n$ and $c$ ($1 \le n, c \le 100$) — the length of arrays $a$ and $b$ and the cost of the second operation.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 100$) — the elements of the first array.

The third line of each test case contains $n$ integers $b_1, b_2, \ldots, b_n$ ($1 \le b_i \le 100$) — the elements of the second array.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 500$）。随后是各测试用例的描述。

每个测试用例的第一行包含两个整数 $n$ 和 $c$（$1 \le n, c \le 100$）—— 分别表示数组 $a$ 和 $b$ 的长度，以及第二种操作的代价。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$1 \le a_i \le 100$）—— 表示第一个数组的元素。

每个测试用例的第三行包含 $n$ 个整数 $b_1, b_2, \ldots, b_n$（$1 \le b_i \le 100$）—— 表示第二个数组的元素。

For each test case, output a single integer representing the minimum number of seconds required to solve the puzzle, or $-1$ if it is impossible to solve the puzzle.

对于每个测试用例，输出一个整数，表示解决该谜题所需的最少秒数；如果无法解决该谜题，则输出 $-1$。

In the first test case, it is impossible to transform $a$ into $b$ using only subtraction because $a_2 \lt b_2$. Let's rearrange the elements of array $a$ as follows: $[5, 2, 3] \Rightarrow [2, 3, 5]$. Now it is enough to subtract one from $a_3$, and we get that array $a$ becomes equal to array $b$ in $5 + 1 = 6$ seconds.

In the second test case, all elements of $a$ are less than all elements of $b$, which means $a$ cannot be transformed into $b$.

In the third test case, you can choose not to rearrange the elements and get an answer of $3$. If you rearrange them at least once, the answer will be at least $4$, so the optimal answer is $3$ seconds.

In the sixth test case, the array can be rearranged as follows: $[14, 20, 20]$. It can be seen that the cost will then be $5 + (14 - 12) + (20 - 18) + (20 - 17) = 12$.

在第一个测试用例中，仅使用减法操作无法将 $a$ 变换为 $b$，因为 $a_2 \lt b_2$。让我们将数组 $a$ 的元素重新排列如下：$[5, 2, 3] \Rightarrow [2, 3, 5]$。此时只需对 $a_3$ 减去 $1$，即可使数组 $a$ 变为与数组 $b$ 相等，总耗时为 $5 + 1 = 6$ 秒。

在第二个测试用例中，$a$ 的所有元素均小于 $b$ 的所有元素，这意味着 $a$ 无法被变换为 $b$。

在第三个测试用例中，你可以选择不重排元素，从而得到答案 $3$。若至少重排一次，答案至少为 $4$，因此最优答案为 $3$ 秒。

在第六个测试用例中，数组可重排为：$[14, 20, 20]$。此时总代价为 $5 + (14 - 12) + (20 - 18) + (20 - 17) = 12$。