human
What is 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 lower_bound(nums,x):
    for i in range(len(nums)):
        if nums[i]>=x:
            return i
    return -1

def check(n,k,num,pos,_n,wid):
    x=num
    nums=dict()
    while x>0:
        nums.setdefault(x%10,0)
        x//=10
    nums=list(nums.keys())
    nums.sort()
    flag=0
    for i in range(pos,wid):
        tmp=int(_n[i])
        x=lower_bound(nums,tmp) if flag==0 else 0
        if x==-1:
            return -1
        if flag==0 and nums[x]>tmp:
            flag=1
        num=num*10+nums[x]
    return num

def work(n,k):
    res=10**11
    _n=str(n)
    wid=len(_n)
    vis=dict()
    tmp=0
    cnt=0
    for i in range(wid):
        num=int(_n[i])
        vis.setdefault(num,0)
        if vis[num]==1:
            tmp=tmp*10+num
            continue
        if cnt==k:
            res=check(n,k,tmp,i,_n,wid)
            if res==-1:
                return work((tmp+1)*(10**(wid-i)),k)
            return res
        cnt+=1
        vis[num]=1
        tmp=tmp*10+num
    return tmp

_t=int(input())
for _c in range(_t):
    n,k=map(int,input().split())
    print(work(n,k))