Redistribution of Digits

You are required to form numbers based on a given set of digits. Each number is also provided with an upper bound. Each digit from the given set must be used exactly once. If the set does not contain a digit, you are not allowed to use it.

First line contains an integer $t$ --- the number of tests.

Each of the next $t$ lines contains a string $s$ --- a given set of digits, integer $n$ --- quantity of numbers which should be formed and $n$ integers $a\_i$ --- upper bounds for numbers. The digits for all numbers $a\_i$ are given in a non-increasing order starting from the most significant digit. The set of digits and the numbers $a\_i$ do not contain a digit $0$.

You are required to output $t$ lines containing the given quantity of numbers corresponding the conditions above. If a solution does not exist you should print "-1". If there are multiple solutions, you may output any of them.

• $1 \le t \le 1000$
• $1 \le |s| \le 500$
• $1 \le n \le 50$
• $1 \le a\_i \le 10^9$