Smallest Hex Multiple

You are given an integer $N$ and a list of $D$ hexadecimal digits. Find the smallest positive integer $X$ that is divisible by $N$ and whose base-16 representation uses only the given digits.

The first line contains the number of test cases $T$ ($1 \le T \le 100$).

Each test case takes two lines. The first line contains $N$ and $D$ in base 10, separated by a space ($1 \le N \le 200000$, $1 \le D \le 16$). The second line contains the allowed hexadecimal digits $d_1, d_2, \dots, d_D$ separated by spaces. Each digit is one of 0 to 9 and a to f, the digits are distinct, and they are given in increasing order.

For each test case, print one line. Print, in base 16, the smallest positive integer $X$ that is divisible by $N$ and uses only the given digits. Write a to f in lowercase and print no leading zeros. If no such number exists, print no solution.

The answer can be very long. It does not always fit in a 64-bit integer, so build it as a string.