human
Give me a Python program to find the minimum integer x such that x ≥ n and the number x is k-beautiful given the following:
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 program to find the minimum integer x such that x ≥ n and the number x is k-beautiful.
 def find_nearest(s, k):
    ln = len(s)
    if max(s[:ln-1]) > s[ln-1]:
        x = list(set(s[:ln-1]))
        x.sort()
        for it in x:
            if it > s[-1]:
                # s[-1] = it
                s = s[:ln-1] + it
                return s
    else:
        # 1778
        for i in range(ln-1, -1, -1):
            x = s[:i]
            while (x[-1] <'9'):
                x = str(int(x)+1)
                if len(set(x)) <=k:
                    if len(set(x)) == k:
                        x = x + (ln-len(x)) * min(set(x))
                        return x
                    else:
                        x = x + (ln-len(x)) * '0'
                        return x

        
def solve(s, k):
    if len(set(str(s))) <=k:
        return s
    s = str(s)
    for i in range(len(s)):
        if len(set(s[:i+1])) > k:
            break
    i+=1
    x = s[:i]
    # print(x)
    x = find_nearest(x, k)
    # print(x)
    # while len(set(x)) >k:
    #     x = str(int(x) +1)
    ans = x + (len(s)-i) * min(set(x))
    return ans
    # k = s[:i]
        

n = int(input())
for _ in range(n):
    s, k = [int(i) for i in input().split()]
    print(solve(s,k))

"""
1
131455 2 -> 1331
177890 2 -> 1
1314 2 -> 1331
"""