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":


 ... Can you provide a Python program to find the minimum integer x such that x ≥ n and the number x is k-beautiful?
assistant
#Here is Python program to find the minimum integer x such that x ≥ n and the number x is k-beautiful.
 def number(L):
    r = 0
    for d in L:
        r = r * 10 + int(d)
    return r

def go(n, i, D, eq):
    if i == len(n):
        return True, []

    if eq:
        for d in D:
            if n[i] == d:
                flag, x = go(n, i + 1, D, True)
                if flag:
                    return True, [d] + x
            if n[i] < d:
                flag, x = go(n, i + 1, D, False)
                if flag:
                    return True, [d] + x

        return False, []
    else:
        flag, x = go(n, i + 1, D, False)
        return True, [D[0]] + x

def find(n, k):
    if len(set(n)) == 1:
        return n
    
    D = []
    for d in map(int, n):
        if d not in D:
            D.append(d)

    if len(D) <= k:
        return n

    U = [D[: k]]

    E = D[: k]
    if (E[-1] + 1) in E:
        E[-1] = 0
    else:
        E[-1] = (E[-1] + 1) % 10
    U.append(E)

    r = 10**20
    for digits in U:
        x = []
        digits.sort()
        flag, x = go(list(map(int, n)), 0, digits, True)
        if flag:
            r = min(r, number(x))

    return r

T = int(input())
for _ in range(T):
    n, k = input().split(' ')
    k = int(k)

                
    print(find(n, k))