human
PYTHON3 solution for "It is a complicated version of problem F1. The difference between them is the constraints (F1: k ≤ 2, F2: k ≤ 10).

You are given an integer n. Find the minimum integer x such that x ≥ 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

The first line contains one integer t (1 ≤ t ≤ 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 ≤ n ≤ 10^9, 1 ≤ k ≤ 10).

Output

For each test case output on a separate line x — the minimum k-beautiful integer such that x ≥ n.

Example

Input

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

Output

2021
181111
34533
724542
999999999
12345678":
assistant
#Here is Python code to find the minimum integer x such that x ≥ n and the number x is k-beautiful.
 def _measure_k(x):
    return len(set(str(x)))

tests_n = int(input())
for i_test in range(tests_n):
    n, k = map(int, input().split())
    
    prefix = n
    while _measure_k(prefix) > k:
        if prefix % 10 == 0:
            prefix //= 10  # the dropped digit can be any digit
        else:
            prefix += 1
    prefix = str(prefix)
    
    tail_digit = '0' if _measure_k(prefix) < k else min(prefix)
    tail = tail_digit * (len(str(n)) - len(prefix))
    
    print(prefix + tail)