CF1367D.Task On The Board

Polycarp wrote on the board a string $s$ containing only lowercase Latin letters ('a'-'z'). This string is known for you and given in the input.

After that, he erased some letters from the string $s$, and he rewrote the remaining letters in any order. As a result, he got some new string $t$. You have to find it with some additional information.

Suppose that the string $t$ has length $m$ and the characters are numbered from left to right from $1$ to $m$. You are given a sequence of $m$ integers: $b_1, b_2, \ldots, b_m$, where $b_i$ is the sum of the distances $|i-j|$ from the index $i$ to all such indices $j$ that $t_j \gt t_i$ (consider that 'a'<'b'<...<'z'). In other words, to calculate $b_i$, Polycarp finds all such indices $j$ that the index $j$ contains a letter that is later in the alphabet than $t_i$ and sums all the values $|i-j|$.

For example, if $t$ = "abzb", then:

• since $t_1$='a', all other indices contain letters which are later in the alphabet, that is: $b_1=|1-2|+|1-3|+|1-4|=1+2+3=6$;
• since $t_2$='b', only the index $j=3$ contains the letter, which is later in the alphabet, that is: $b_2=|2-3|=1$;
• since $t_3$='z', then there are no indexes $j$ such that $t_j \gt t_i$, thus $b_3=0$;
• since $t_4$='b', only the index $j=3$ contains the letter, which is later in the alphabet, that is: $b_4=|4-3|=1$.

Thus, if $t$ = "abzb", then $b=[6,1,0,1]$.

Given the string $s$ and the array $b$, find any possible string $t$ for which the following two requirements are fulfilled simultaneously:

• $t$ is obtained from $s$ by erasing some letters (possibly zero) and then writing the rest in any order;
• the array, constructed from the string $t$ according to the rules above, equals to the array $b$ specified in the input data.

波利卡普在黑板上写了一个仅包含小写拉丁字母（'a'–'z'）的字符串 $s$。该字符串已知，且作为输入给出。

随后，他从字符串 $s$ 中擦除了若干字母，并将剩余字母以任意顺序重新书写，从而得到一个新字符串 $t$。你需要根据一些附加信息找出这个字符串 $t$。

假设字符串 $t$ 的长度为 $m$，其字符从左到右编号为 $1$ 到 $m$。你将获得一个由 $m$ 个整数组成的序列：$b_1, b_2, \ldots, b_m$，其中 $b_i$ 表示所有满足 $t_j > t_i$ 的下标 $j$ 到下标 $i$ 的距离之和 $|i-j|$（约定 'a' < 'b' < ... < 'z'）。换言之，为计算 $b_i$，波利卡普找出所有满足 $t_j$ 在字母表中位于 $t_i$ 之后的下标 $j$，并将所有 $|i-j|$ 的值相加。

例如，若 $t = \text{``abzb''}$，则：

• 由于 $t_1 = \text{'a'}$，其余所有下标处的字母均在字母表中位于 'a' 之后，即：$b_1 = |1-2| + |1-3| + |1-4| = 1 + 2 + 3 = 6$；
• 由于 $t_2 = \text{'b'}$，仅下标 $j = 3$ 处的字母在字母表中位于 'b' 之后，即：$b_2 = |2-3| = 1$；
• 由于 $t_3 = \text{'z'}$，不存在满足 $t_j > t_i$ 的下标 $j$，故 $b_3 = 0$；
• 由于 $t_4 = \text{'b'}$，仅下标 $j = 3$ 处的字母在字母表中位于 'b' 之后，即：$b_4 = |4-3| = 1$。

因此，若 $t = \text{``abzb''}$，则 $b = [6,1,0,1]$。

给定字符串 $s$ 和数组 $b$，请找出任意一个可能的字符串 $t$，使得以下两个条件同时成立：

• $t$ 是通过从 $s$ 中擦除若干字母（可能为零个）后，将剩余字母以任意顺序重排而得到的；
• 按照上述规则由字符串 $t$ 构造出的数组等于输入中指定的数组 $b$。

The first line contains an integer $q$ ($1 \le q \le 100$) — the number of test cases in the test. Then $q$ test cases follow.

Each test case consists of three lines:

• the first line contains string $s$, which has a length from $1$ to $50$ and consists of lowercase English letters;
• the second line contains positive integer $m$ ($1 \le m \le |s|$), where $|s|$ is the length of the string $s$, and $m$ is the length of the array $b$;
• the third line contains the integers $b_1, b_2, \dots, b_m$ ($0 \le b_i \le 1225$).

It is guaranteed that in each test case an answer exists.

第一行包含一个整数 $q$（$1 \le q \le 100$），表示测试用例的数量。随后是 $q$ 个测试用例。

每个测试用例由三行组成：

• 第一行包含字符串 $s$，其长度为 $1$ 到 $50$，且仅由小写英文字母组成；
• 第二行包含正整数 $m$（$1 \le m \le |s|$），其中 $|s|$ 表示字符串 $s$ 的长度，$m$ 为数组 $b$ 的长度；
• 第三行包含整数 $b_1, b_2, \dots, b_m$（$0 \le b_i \le 1225$）。

保证每个测试用例均存在解。

Output $q$ lines: the $k$-th of them should contain the answer (string $t$) to the $k$-th test case. It is guaranteed that an answer to each test case exists. If there are several answers, output any.

输出 $q$ 行：第 $k$ 行应包含第 $k$ 个测试用例的答案（字符串 $t$）。保证每个测试用例均存在答案。若存在多个答案，输出任意一个即可。

In the first test case, such strings $t$ are suitable: "aac', "aab".

In the second test case, such trings $t$ are suitable: "a", "b", "c".

In the third test case, only the string $t$ equals to "aba" is suitable, but the character 'b' can be from the second or third position.

在第一个测试用例中，满足条件的字符串 $t$ 有："aac"、"aab"。

在第二个测试用例中，满足条件的字符串 $t$ 有："a"、"b"、"c"。

在第三个测试用例中，唯一满足条件的字符串 $t$ 是 "aba"，但其中的字符 'b' 可以来自原字符串的第二个或第三个位置。