#include <bits/stdc++.h>
using namespace std;
bool issorted(long long arr[], int n) {
  if (n == 1) return true;
  return (arr[0] < arr[1] and issorted(arr + 1, n - 1));
}
void solve() {
  long long n, k;
  cin >> n >> k;
  long long a[n], sum = 0;
  k++;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    a[i] = powl(10LL, a[i]);
  }
  sort(a, a + n);
  for (int i = 1; i < n; i++) {
    long long tmp = k;
    k -= ((a[i] / a[i - 1]) - 1);
    if (k >= 0) {
      sum += ((a[i] / a[i - 1]) - 1) * a[i - 1];
    } else {
      sum += a[i - 1] * tmp;
      break;
    }
  }
  if (k >= 0) {
    sum += a[n - 1] * k;
  }
  cout << sum << '\n';
}
int main() {
  int t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
}

### Prompt

Develop a solution in CPP to the problem described below:

In Berland, n different types of banknotes are used. Banknotes of the i-th type have denomination 10^{a_i} burles (burles are the currency used in Berland); the denomination of banknotes of the first type is exactly 1.

Let's denote f(s) as the minimum number of banknotes required to represent exactly s burles. For example, if the denominations of banknotes used in Berland are 1, 10 and 100, then f(59) = 14: 9 banknotes with denomination of 1 burle and 5 banknotes with denomination of 10 burles can be used to represent exactly 9 ⋅ 1 + 5 ⋅ 10 = 59 burles, and there's no way to do it with fewer banknotes.

For a given integer k, find the minimum positive number of burles s that cannot be represented with k or fewer banknotes (that is, f(s) > k).

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — number of test cases.

The first line of each test case contains two integers n and k (1 ≤ n ≤ 10; 1 ≤ k ≤ 10^9).

The next line contains n integers a_1, a_2, ..., a_n (0 = a_1 < a_2 < ... < a_n ≤ 9).

Output

For each test case, print one integer — the minimum positive number of burles s that cannot be represented with k or fewer banknotes.

Example

Input


4
3 13
0 1 2
2 777
0 4
3 255
0 1 3
10 1000000000
0 1 2 3 4 5 6 7 8 9


Output


59
778
148999
999999920999999999

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
bool issorted(long long arr[], int n) {
  if (n == 1) return true;
  return (arr[0] < arr[1] and issorted(arr + 1, n - 1));
}
void solve() {
  long long n, k;
  cin >> n >> k;
  long long a[n], sum = 0;
  k++;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    a[i] = powl(10LL, a[i]);
  }
  sort(a, a + n);
  for (int i = 1; i < n; i++) {
    long long tmp = k;
    k -= ((a[i] / a[i - 1]) - 1);
    if (k >= 0) {
      sum += ((a[i] / a[i - 1]) - 1) * a[i - 1];
    } else {
      sum += a[i - 1] * tmp;
      break;
    }
  }
  if (k >= 0) {
    sum += a[n - 1] * k;
  }
  cout << sum << '\n';
}
int main() {
  int t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
}

```