New Year and Naming

【题目描述】 新年快乐！在韩国 $2020$ 年也被称为庆州年(Year Gyeongja，경자년，gyeongja-nyeon)。该名字从何而来？让我们简要的看一下韩国传统的给年份命名的系统 $Gapja \ system$。 这里有两个序列，元素都是字符串，长度分别为 $n$、$m$，元素分别为 $s_1,s_2,s_3,\dots,s_n$、$t_1,t_2,t_3,\dots,t_n$。这些字符串只包含小写字母。可能有相同的字符串。 我们将在不改变顺序的前提下将字符串 $x$ 与 $y$ 写下来得到的字符串称作字符串 $x$ 与字符串 $y$ 的串联。例如：“code”和“forces”的串联字符串为“codeforces”。 第一年被命名为 $s_1$ 和 $t_1$ 的串联，当年份增加一时，两个被串联在一起的字符串下标加一。如果超出了字符串序列的长度，则超出长度的那一个序列回到序列开始的位置，也就是下标为 $1$ 的位置。 例如：如果 $n=3,m=4,s=$\{"a","b","c"\} , $t=\{"d","e","f","g"\}$，产生的年份的名称如下表所示 注意年份的名称可以重复。 给你两个序列长度分别为 $n$，$m$ 和 $q$ 个询问。每个查询给你当前的年份，请你从 $Gapja \ system$ 系统中找出它的名字。 【输入格式】 第一行有两个整数 $n,m \ (1 \le n,m \le 20)$。 下一行有由空格分隔的 $n$ 个字符串 $s_1,s_2,s_3,\dots,s_n$，每个字符串仅有小写字母构成，字符串的长度在一到十之间。 下一行有由空格分隔的 $m$ 个字符串 $t_1,t_2,t_3,\dots,t_m$，每个字符串仅有小写字母构成，字符串的长度在一到十之间。 所给的字符串中可能有重复。 下一行一个整数 $q \ (1 \le q \le 2020)$ 表示询问的个数。 接下来的 $q$ 行，每行一个整数 $y \ (1 \le y \le 10 ^ 9)$，表示询问你年份 $y$ 的名称。 【输出格式】 输出共 $q$ 行，第 $i$ 行表示第 $i$ 个询问的答案。 【说明/提示】 **数据范围** 字符串序列的长度 $n,m$ 满足 $1 \le n,m \le 20$。 询问个数 $q$ 满足 $1 \le q \le 2020$。 询问的年份 $y$ 满足 $1 \le y \le 10 ^ 9$ **关于样例** 第一个样例使用的是实际的 $Gapja \ system$。这些字符串一般是数字或动物的名称。 translated by [yu__xuan](https://www.luogu.com.cn/user/142110)。

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?

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.

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

10 12
sin im gye gap eul byeong jeong mu gi gyeong
yu sul hae ja chuk in myo jin sa o mi sin
14
1
2
3
4
10
11
12
13
73
2016
2017
2018
2019
2020

sinyu
imsul
gyehae
gapja
gyeongo
sinmi
imsin
gyeyu
gyeyu
byeongsin
jeongyu
musul
gihae
gyeongja

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.