F2. Nearest Beautiful Number (hard version)time limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputIt is a complicated version of problem F1. The difference between them is the constraints (F1: k \le 2, F2: k \le 10).You are given an integer n. Find the minimum integer x such that x \ge n and the number x is k-beautiful.A number is called k-beautiful if its decimal representation having no leading zeroes contains no more than k different digits. E.g. if k = 2, the numbers 3434443, 55550, 777 and 21 are k-beautiful whereas the numbers 120, 445435 and 998244353 are not.InputThe first line contains one integer t (1 \le t \le 10^4) — the number of test cases. Then t test cases follow.Each test case consists of one line containing two integers n and k (1 \le n \le 10^9, 1 \le k \le 10).OutputFor each test case output on a separate line x — the minimum k-beautiful integer such that x \ge n.ExampleInput
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
Output
2021
181111
34533
724542
999999999
12345678

6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10

2021 181111 34533 724542 999999999 12345678 
['bitmasks', 'brute force', 'constructive algorithms', 'dfs and similar', 'dp', 'greedy', '*2100']