CF1917C.Watering an Array

You have an array of integers $a_1, a_2, \ldots, a_n$ of length $n$. On the $i$-th of the next $d$ days you are going to do exactly one of the following two actions:

• Add $1$ to each of the first $b_i$ elements of the array $a$ (i.e., set $a_j := a_j + 1$ for each $1 \le j \le b_i$).
• Count the elements which are equal to their position (i.e., the $a_j = j$). Denote the number of such elements as $c$. Then, you add $c$ to your score, and reset the entire array $a$ to a $0$-array of length $n$ (i.e., set $[a_1, a_2, \ldots, a_n] := [0, 0, \ldots, 0]$).

Your score is equal to $0$ in the beginning. Note that on each day you should perform exactly one of the actions above: you cannot skip a day or perform both actions on the same day.

What is the maximum score you can achieve at the end?

Since $d$ can be quite large, the sequence $b$ is given to you in the compressed format:

• You are given a sequence of integers $v_1, v_2, \ldots, v_k$. The sequence $b$ is a concatenation of infinitely many copies of $v$: $b = [v_1, v_2, \ldots, v_k, v_1, v_2, \ldots, v_k, \ldots]$.

你有一个长度为 $n$ 的整数数组 $a_1, a_2, \ldots, a_n$。在接下来的 $d$ 天中，第 $i$ 天你恰好执行以下两种操作之一：

• 将数组 $a$ 的前 $b_i$ 个元素各加 $1$（即对每个 $1 \le j \le b_i$，令 $a_j := a_j + 1$）；
• 统计满足“元素值等于其位置下标”的元素个数（即满足 $a_j = j$ 的 $j$ 的个数），记该数量为 $c$；然后将 $c$ 加入你的得分，并将整个数组 $a$ 重置为全零数组（即令 $[a_1, a_2, \ldots, a_n] := [0, 0, \ldots, 0]$）。

初始得分为 $0$。注意：每天必须且只能执行上述两个操作之一，不可跳过某天，也不可在同一天执行两个操作。

最终你能获得的最大得分是多少？

由于 $d$ 可能非常大，序列 $b$ 以压缩格式给出：

• 你将获得一个整数序列 $v_1, v_2, \ldots, v_k$；序列 $b$ 是由无限次重复 $v$ 得到的：$b = [v_1, v_2, \ldots, v_k, v_1, v_2, \ldots, v_k, \ldots]$。

The first line contains a single integer $t$ ($1 \le t \le 10^3$) — the number of test cases.

The first line of each test case contains three integers $n$, $k$ and $d$ ($1 \le n \le 2000$, $1 \le k \le 10^5$, $k \le d \le 10^9$) — the length of the array $a$, the length of the sequence $v$ and the number of days you are going to perform operations on.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le n$) — the array $a$.

The third line of each test case contains $k$ integers $v_1, v_2, \ldots, v_k$ ($1 \le v_i \le n$) — the sequence $v$.

It is guaranteed that the sum of $n$ over all test cases doesn't exceed $2000$ and the sum of $k$ over all test cases doesn't exceed $10^5$.

第一行包含一个整数 $t$（$1 \le t \le 10^3$）—— 测试用例的数量。

每个测试用例的第一行包含三个整数 $n$、$k$ 和 $d$（$1 \le n \le 2000$，$1 \le k \le 10^5$，$k \le d \le 10^9$）—— 分别表示数组 $a$ 的长度、序列 $v$ 的长度，以及你将执行操作的天数。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$0 \le a_i \le n$）—— 数组 $a$。

每个测试用例的第三行包含 $k$ 个整数 $v_1, v_2, \ldots, v_k$（$1 \le v_i \le n$）—— 序列 $v$。

保证所有测试用例中 $n$ 的总和不超过 $2000$，且所有测试用例中 $k$ 的总和不超过 $10^5$。

For each test case, output one integer: the maximum score you can achieve at the end of the $d$-th day.

对于每个测试用例，输出一个整数：在第 $d$ 天结束时你能获得的最高分数。

In the first test case, the sequence $b$ is equal to $[1, 3, 2, 3, 1, 3, 2, 3, \ldots]$ and one of the optimal solutions for this case is as follows:

• Perform the operation of the second type on the $1$-st day: your score increases by $3$ and array $a$ becomes equal to $[0, 0, 0]$.
• Perform the operation of the first type on the $2$-nd day: array $a$ becomes equal to $[1, 1, 1]$.
• Perform the operation of the first type on the $3$-rd day: array $a$ becomes equal to $[2, 2, 1]$.
• Perform the operation of the second type on the $4$-th day: your score increases by $1$ and array $a$ becomes equal to $[0, 0, 0]$.

It can be shown that it is impossible to score more than $4$, so the answer is $4$.

In the second test case, the sequence $b$ is equal to $[6, 6, 6, 6, \ldots]$. One of the ways to score $3$ is to perform operations of the first type on the $1$-st and the $3$-rd days and to perform an operation of the second type on the $2$-nd day.

在第一个测试用例中，序列 $b$ 等于 $[1, 3, 2, 3, 1, 3, 2, 3, \ldots]$，该测试用例的一个最优解如下：

• 在第 $1$ 天执行第二种操作：你的得分增加 $3$，数组 $a$ 变为 $[0, 0, 0]$。
• 在第 $2$ 天执行第一种操作：数组 $a$ 变为 $[1, 1, 1]$。
• 在第 $3$ 天执行第一种操作：数组 $a$ 变为 $[2, 2, 1]$。
• 在第 $4$ 天执行第二种操作：你的得分增加 $1$，数组 $a$ 变为 $[0, 0, 0]$。

可以证明，不可能获得超过 $4$ 的得分，因此答案为 $4$。

在第二个测试用例中，序列 $b$ 等于 $[6, 6, 6, 6, \ldots]$。一种获得 $3$ 分的方法是：在第 $1$ 天和第 $3$ 天执行第一种操作，在第 $2$ 天执行第二种操作。