You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
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 $$$t_j > t_i$$$ (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 $$$t_j>t_i$$$, 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.

## Input Format
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.

## Output Format
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.

## Examples
```input
4
abac
3
2 1 0
abc
1
0
abba
3
1 0 1
ecoosdcefr
10
38 13 24 14 11 5 3 24 17 0
```
```output
aac
b
aba
codeforces
```

## Note
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.

Now solve the problem and return the code.