Nearest Beautiful Number (hard version) solution codeforces

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It is a complicated version of problem F1. The difference between them is the constraints (F1: $k \leq 2$ , F2: $k \leq 10$ ).

You are given an integer $n$ . Find the minimum integer $x$ such that $x \geq n$ 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.

Input Nearest Beautiful Number (hard version) solution codeforces

The first line contains one integer $t$ ( $1 \leq t \leq 10^{4}$ ) — the number of test cases. Then $t$ test cases follow.

Each test case consists of one line containing two integers $n$ and $k$ ( $1 \leq n \leq 10^{9}$ , $1 \leq k \leq 10$ ).

Output

For each test case output on a separate line $x$ — the minimum $k$ –beautiful integer such that $x \geq n$ .

Example

input

Copy

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

output

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Nearest Beautiful Number (hard version) solution codeforces

For Solution

Click Here!

For Solution

Click Here!

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