#include <bits/stdc++.h>
using namespace std;
int difdig(int x) {
  int tmp = 0;
  while (x != 0) {
    tmp |= (1 << (x % 10));
    x /= 10;
  }
  return __builtin_popcount(tmp);
}
int main() {
  int _;
  cin >> _;
  while (_--) {
    int n, k;
    cin >> n >> k;
    while (difdig(n) > k) {
      int r = 1;
      int c = n;
      while (difdig(c) > k) {
        c /= 10;
        r *= 10;
      }
      r /= 10;
      n = (n / r + 1) * r;
    }
    cout << n << '\n';
  }
  return 0;
}

### Prompt

Your challenge is to write a Cpp solution to the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int difdig(int x) {
  int tmp = 0;
  while (x != 0) {
    tmp |= (1 << (x % 10));
    x /= 10;
  }
  return __builtin_popcount(tmp);
}
int main() {
  int _;
  cin >> _;
  while (_--) {
    int n, k;
    cin >> n >> k;
    while (difdig(n) > k) {
      int r = 1;
      int c = n;
      while (difdig(c) > k) {
        c /= 10;
        r *= 10;
      }
      r /= 10;
      n = (n / r + 1) * r;
    }
    cout << n << '\n';
  }
  return 0;
}

```