#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007;
const unsigned gen_seed =
    std::chrono::system_clock::now().time_since_epoch().count();
std::mt19937_64 gen(gen_seed);
int test(int n) {
  std::vector<int> cnt(10, 0);
  int ret = 0;
  while (n > 0) {
    int k = n % 10;
    n /= 10;
    if (cnt[k] == 0) ret++;
    cnt[k]++;
  }
  return ret;
}
int mind(int n) {
  std::vector<int> cnt(10, 0);
  while (n > 0) {
    cnt[n % 10] = 1;
    n /= 10;
  }
  for (int i = 0; i < 10; i++)
    if (cnt[i] == 1) return i;
  return -1;
}
int get(int n, int k) {
  while (1) {
    if (test(n) <= k) return n;
    if (n % 10 == 0) {
      int res = get(n / 10, k);
      return 10 * res + mind(res);
    }
    n++;
  }
}
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    int n, k;
    scanf("%d %d", &n, &k);
    printf("%d\n", get(n, k));
  }
}

### Prompt

Develop a solution in cpp to the problem described below:

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;
const long long mod = 1000000007;
const unsigned gen_seed =
    std::chrono::system_clock::now().time_since_epoch().count();
std::mt19937_64 gen(gen_seed);
int test(int n) {
  std::vector<int> cnt(10, 0);
  int ret = 0;
  while (n > 0) {
    int k = n % 10;
    n /= 10;
    if (cnt[k] == 0) ret++;
    cnt[k]++;
  }
  return ret;
}
int mind(int n) {
  std::vector<int> cnt(10, 0);
  while (n > 0) {
    cnt[n % 10] = 1;
    n /= 10;
  }
  for (int i = 0; i < 10; i++)
    if (cnt[i] == 1) return i;
  return -1;
}
int get(int n, int k) {
  while (1) {
    if (test(n) <= k) return n;
    if (n % 10 == 0) {
      int res = get(n / 10, k);
      return 10 * res + mind(res);
    }
    n++;
  }
}
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    int n, k;
    scanf("%d %d", &n, &k);
    printf("%d\n", get(n, k));
  }
}

```