CF1284A.New Year and Naming

Happy new year! The year 2020 is also known as Year Gyeongja (경자년, gyeongja-nyeon) in Korea. Where did the name come from? Let's briefly look at the Gapja system, which is traditionally used in Korea to name the years.

There are two sequences of $n$ strings $s_1, s_2, s_3, \ldots, s_{n}$ and $m$ strings $t_1, t_2, t_3, \ldots, t_{m}$. These strings contain only lowercase letters. There might be duplicates among these strings.

Let's call a concatenation of strings $x$ and $y$ as the string that is obtained by writing down strings $x$ and $y$ one right after another without changing the order. For example, the concatenation of the strings "code" and "forces" is the string "codeforces".

The year 1 has a name which is the concatenation of the two strings $s_1$ and $t_1$. When the year increases by one, we concatenate the next two strings in order from each of the respective sequences. If the string that is currently being used is at the end of its sequence, we go back to the first string in that sequence.

For example, if $n = 3, m = 4, s = ${"a", "b", "c"}, $t =$ {"d", "e", "f", "g"}, the following table denotes the resulting year names. Note that the names of the years may repeat.

You are given two sequences of strings of size $n$ and $m$ and also $q$ queries. For each query, you will be given the current year. Could you find the name corresponding to the given year, according to the Gapja system?

新年快乐！2020 年在韩国也被称为“庚子年”（Gyeongja-nyeon，경자년）。这个名字从何而来？让我们简要了解一下韩国传统上用于纪年的“干支”（Gapja）系统。

现有两个字符串序列：长度为 $n$ 的序列 $s_1, s_2, s_3, \ldots, s_{n}$ 和长度为 $m$ 的序列 $t_1, t_2, t_3, \ldots, t_{m}$。这些字符串仅由小写字母组成，且各序列内部可能存在重复字符串。

我们定义字符串 $x$ 与 $y$ 的拼接（concatenation）为将 $x$ 与 $y$ 按原有顺序前后相连所得到的字符串。例如，字符串 "code" 与 "forces" 的拼接结果为 "codeforces"。

第 1 年的名称为字符串 $s_1$ 与 $t_1$ 的拼接结果。此后每增加一年，就依次从各自序列中取下一个字符串进行拼接；若当前所用字符串已位于其所在序列末尾，则循环回到该序列的第一个字符串。

例如，当 $n = 3$、$m = 4$、$s = ${"a", "b", "c"}、$t =$ {"d", "e", "f", "g"} 时，下表列出了对应年份的名称（注意：不同年份的名称可能重复）。

现给你两个长度分别为 $n$ 和 $m$ 的字符串序列，以及 $q$ 个查询。对每个查询，你将获得一个年份编号，请根据干支（Gapja）系统，找出该年份对应的名称。

The first line contains two integers $n, m$ ($1 \le n, m \le 20$).

The next line contains $n$ strings $s_1, s_2, \ldots, s_{n}$. Each string contains only lowercase letters, and they are separated by spaces. The length of each string is at least $1$ and at most $10$.

The next line contains $m$ strings $t_1, t_2, \ldots, t_{m}$. Each string contains only lowercase letters, and they are separated by spaces. The length of each string is at least $1$ and at most $10$.

Among the given $n + m$ strings may be duplicates (that is, they are not necessarily all different).

The next line contains a single integer $q$ ($1 \le q \le 2\,020$).

In the next $q$ lines, an integer $y$ ($1 \le y \le 10^9$) is given, denoting the year we want to know the name for.

第一行包含两个整数 $n, m$（$1 \le n, m \le 20$）。

第二行包含 $n$ 个字符串 $s_1, s_2, \ldots, s_{n}$。每个字符串仅由小写字母组成，且以空格分隔。每个字符串的长度至少为 $1$，至多为 $10$。

第三行包含 $m$ 个字符串 $t_1, t_2, \ldots, t_{m}$。每个字符串仅由小写字母组成，且以空格分隔。每个字符串的长度至少为 $1$，至多为 $10$。

在给定的 $n + m$ 个字符串中可能存在重复（即它们不一定互不相同）。

第四行包含一个整数 $q$（$1 \le q \le 2\,020$）。

接下来的 $q$ 行中，每行给出一个整数 $y$（$1 \le y \le 10^9$），表示我们想查询其对应名称的年份。

Print $q$ lines. For each line, print the name of the year as per the rule described above.

输出 $q$ 行。对于每一行，按照上述规则输出该年的名称。

The first example denotes the actual names used in the Gapja system. These strings usually are either a number or the name of some animal.

第一个示例表示 Gapja 系统中实际使用的名字。这些字符串通常要么是一个数字，要么是某种动物的名称。