#P1560F2. Nearest Beautiful Number (hard version)
Nearest Beautiful Number (hard version)
Description
It 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.
The 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 $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
Input
The 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 $k$ ($1 \le n \le 10^9$, $1 \le k \le 10$).
Output
For each test case output on a separate line $x$ — the minimum $k$-beautiful integer such that $x \ge n$.
Samples
6
2021 3
177890 2
34512 3
724533 4
998244353 1
12345678 10
2021
181111
34533
724542
999999999
12345678