#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
double EPS = 1e-9;
int INF = 1000000005;
long long INFF = 1000000000000000005ll;
double PI = acos(-1);
int dirx[8] = {-1, 0, 0, 1, -1, -1, 1, 1};
int diry[8] = {0, 1, -1, 0, -1, 1, -1, 1};
template <typename T>
int SIZE(T(&t)) {
  return t.size();
}
template <typename T, size_t N>
int SIZE(T (&t)[N]) {
  return N;
}
string to_string(char t) { return "'" + string({t}) + "'"; }
string to_string(bool t) { return t ? "true" : "false"; }
string to_string(const string &t, int x1 = 0, int x2 = 1e9) {
  string ret = "";
  for (int i = min(x1, SIZE(t)), _i = min(x2, SIZE(t) - 1); i <= _i; ++i) {
    ret += t[i];
  }
  return '"' + ret + '"';
}
string to_string(const char *t) {
  string ret(t);
  return to_string(ret);
}
template <size_t N>
string to_string(const bitset<N> &t, int x1 = 0, int x2 = 1e9) {
  string ret = "";
  for (int i = min(x1, SIZE(t)); i <= min(x2, SIZE(t) - 1); ++i) {
    ret += t[i] + '0';
  }
  return to_string(ret);
}
template <typename T, typename... Coords>
string to_string(const T(&t), int x1 = 0, int x2 = 1e9, Coords... C);
template <typename T, typename S>
string to_string(const pair<T, S> &t) {
  return "(" + to_string(t.first) + ", " + to_string(t.second) + ")";
}
template <typename T, typename... Coords>
string to_string(const T(&t), int x1, int x2, Coords... C) {
  string ret = "[";
  x1 = min(x1, SIZE(t));
  auto e = begin(t);
  advance(e, x1);
  for (int i = x1, _i = min(x2, SIZE(t) - 1); i <= _i; ++i) {
    ret += to_string(*e, C...) + (i != _i ? ", " : "");
    e = next(e);
  }
  return ret + "]";
}
template <int Index, typename... Ts>
struct print_tuple {
  string operator()(const tuple<Ts...> &t) {
    string ret = print_tuple<Index - 1, Ts...>{}(t);
    ret += (Index ? ", " : "");
    return ret + to_string(get<Index>(t));
  }
};
template <typename... Ts>
struct print_tuple<0, Ts...> {
  string operator()(const tuple<Ts...> &t) { return to_string(get<0>(t)); }
};
template <typename... Ts>
string to_string(const tuple<Ts...> &t) {
  const auto Size = tuple_size<tuple<Ts...>>::value;
  return print_tuple<Size - 1, Ts...>{}(t);
}
void dbgr() { ; }
template <typename Heads, typename... Tails>
void dbgr(Heads H, Tails... T) {
  cout << to_string(H) << " | ";
  dbgr(T...);
}
void dbgs() { ; }
template <typename Heads, typename... Tails>
void dbgs(Heads H, Tails... T) {
  cout << H << " ";
  dbgs(T...);
}
const int MOD = 1000000007;
template <typename T_vector>
void output_vector(const T_vector &v, bool line_break = false,
                   bool add_one = false, int start = -1, int end = -1) {
  if (start < 0) start = 0;
  if (end < 0) end = int(v.size());
  for (int i = start; i < end; i++) {
    cout << v[i] + (add_one ? 1 : 0)
         << (line_break    ? '\n'
             : i < end - 1 ? ' '
                           : '\n');
  }
}
void solve() {
  long long n, k;
  cin >> n >> k;
  vector<long long> a(n);
  for (int(i) = (0); (i) < (n); ++(i)) {
    cin >> a[i];
    --a[i];
  }
  vector<vector<long long>> dp(n + 1, vector<long long>(n, -INFF));
  dp[0][0] = 0;
  for (int(i) = (0); (i) < (n); ++(i)) {
    for (int(j) = (0); (j) < (n); ++(j)) {
      if (dp[i][j] < 0) continue;
      dp[i + 1][j] = max(dp[i + 1][j], dp[i][j] + (a[i] == i - j));
      if (j + 1 < n) dp[i + 1][j + 1] = max(dp[i + 1][j + 1], dp[i][j]);
    }
  }
  long long ans = n;
  for (int(j) = (0); (j) < (n); ++(j)) {
    if (dp[n][j] >= k) {
      ans = min(ans, (long long)j);
    }
  }
  cout << (ans == n ? -1 : ans) << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int tc;
  cin >> tc;
  while (tc--) solve();
  return 0;
}

### Prompt

In cpp, your task is to solve the following problem:

Consider a sequence of integers a_1, a_2, …, a_n. In one move, you can select any element of the sequence and delete it. After an element is deleted, all elements to the right are shifted to the left by 1 position, so there are no empty spaces in the sequence. So after you make a move, the sequence's length decreases by 1. The indices of the elements after the move are recalculated.

E. g. let the sequence be a=[3, 2, 2, 1, 5]. Let's select the element a_3=2 in a move. Then after the move the sequence will be equal to a=[3, 2, 1, 5], so the 3-rd element of the new sequence will be a_3=1 and the 4-th element will be a_4=5.

You are given a sequence a_1, a_2, …, a_n and a number k. You need to find the minimum number of moves you have to make so that in the resulting sequence there will be at least k elements that are equal to their indices, i. e. the resulting sequence b_1, b_2, …, b_m will contain at least k indices i such that b_i = i.

Input

The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.

Each test case consists of two consecutive lines. The first line contains two integers n and k (1 ≤ k ≤ n ≤ 2000). The second line contains a sequence of integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n). The numbers in the sequence are not necessarily different.

It is guaranteed that the sum of n over all test cases doesn't exceed 2000.

Output

For each test case output in a single line:

  * -1 if there's no desired move sequence; 
  * otherwise, the integer x (0 ≤ x ≤ n) — the minimum number of the moves to be made so that the resulting sequence will contain at least k elements that are equal to their indices. 

Example

Input


4
7 6
1 1 2 3 4 5 6
5 2
5 1 3 2 3
5 2
5 5 5 5 4
8 4
1 2 3 3 2 2 5 5


Output


1
2
-1
2

Note

In the first test case the sequence doesn't satisfy the desired condition, but it can be provided by deleting the first element, hence the sequence will be [1, 2, 3, 4, 5, 6] and 6 elements will be equal to their indices.

In the second test case there are two ways to get the desired result in 2 moves: the first one is to delete the 1-st and the 3-rd elements so that the sequence will be [1, 2, 3] and have 3 elements equal to their indices; the second way is to delete the 2-nd and the 3-rd elements to get the sequence [5, 2, 3] with 2 desired elements.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
double EPS = 1e-9;
int INF = 1000000005;
long long INFF = 1000000000000000005ll;
double PI = acos(-1);
int dirx[8] = {-1, 0, 0, 1, -1, -1, 1, 1};
int diry[8] = {0, 1, -1, 0, -1, 1, -1, 1};
template <typename T>
int SIZE(T(&t)) {
  return t.size();
}
template <typename T, size_t N>
int SIZE(T (&t)[N]) {
  return N;
}
string to_string(char t) { return "'" + string({t}) + "'"; }
string to_string(bool t) { return t ? "true" : "false"; }
string to_string(const string &t, int x1 = 0, int x2 = 1e9) {
  string ret = "";
  for (int i = min(x1, SIZE(t)), _i = min(x2, SIZE(t) - 1); i <= _i; ++i) {
    ret += t[i];
  }
  return '"' + ret + '"';
}
string to_string(const char *t) {
  string ret(t);
  return to_string(ret);
}
template <size_t N>
string to_string(const bitset<N> &t, int x1 = 0, int x2 = 1e9) {
  string ret = "";
  for (int i = min(x1, SIZE(t)); i <= min(x2, SIZE(t) - 1); ++i) {
    ret += t[i] + '0';
  }
  return to_string(ret);
}
template <typename T, typename... Coords>
string to_string(const T(&t), int x1 = 0, int x2 = 1e9, Coords... C);
template <typename T, typename S>
string to_string(const pair<T, S> &t) {
  return "(" + to_string(t.first) + ", " + to_string(t.second) + ")";
}
template <typename T, typename... Coords>
string to_string(const T(&t), int x1, int x2, Coords... C) {
  string ret = "[";
  x1 = min(x1, SIZE(t));
  auto e = begin(t);
  advance(e, x1);
  for (int i = x1, _i = min(x2, SIZE(t) - 1); i <= _i; ++i) {
    ret += to_string(*e, C...) + (i != _i ? ", " : "");
    e = next(e);
  }
  return ret + "]";
}
template <int Index, typename... Ts>
struct print_tuple {
  string operator()(const tuple<Ts...> &t) {
    string ret = print_tuple<Index - 1, Ts...>{}(t);
    ret += (Index ? ", " : "");
    return ret + to_string(get<Index>(t));
  }
};
template <typename... Ts>
struct print_tuple<0, Ts...> {
  string operator()(const tuple<Ts...> &t) { return to_string(get<0>(t)); }
};
template <typename... Ts>
string to_string(const tuple<Ts...> &t) {
  const auto Size = tuple_size<tuple<Ts...>>::value;
  return print_tuple<Size - 1, Ts...>{}(t);
}
void dbgr() { ; }
template <typename Heads, typename... Tails>
void dbgr(Heads H, Tails... T) {
  cout << to_string(H) << " | ";
  dbgr(T...);
}
void dbgs() { ; }
template <typename Heads, typename... Tails>
void dbgs(Heads H, Tails... T) {
  cout << H << " ";
  dbgs(T...);
}
const int MOD = 1000000007;
template <typename T_vector>
void output_vector(const T_vector &v, bool line_break = false,
                   bool add_one = false, int start = -1, int end = -1) {
  if (start < 0) start = 0;
  if (end < 0) end = int(v.size());
  for (int i = start; i < end; i++) {
    cout << v[i] + (add_one ? 1 : 0)
         << (line_break    ? '\n'
             : i < end - 1 ? ' '
                           : '\n');
  }
}
void solve() {
  long long n, k;
  cin >> n >> k;
  vector<long long> a(n);
  for (int(i) = (0); (i) < (n); ++(i)) {
    cin >> a[i];
    --a[i];
  }
  vector<vector<long long>> dp(n + 1, vector<long long>(n, -INFF));
  dp[0][0] = 0;
  for (int(i) = (0); (i) < (n); ++(i)) {
    for (int(j) = (0); (j) < (n); ++(j)) {
      if (dp[i][j] < 0) continue;
      dp[i + 1][j] = max(dp[i + 1][j], dp[i][j] + (a[i] == i - j));
      if (j + 1 < n) dp[i + 1][j + 1] = max(dp[i + 1][j + 1], dp[i][j]);
    }
  }
  long long ans = n;
  for (int(j) = (0); (j) < (n); ++(j)) {
    if (dp[n][j] >= k) {
      ans = min(ans, (long long)j);
    }
  }
  cout << (ans == n ? -1 : ans) << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int tc;
  cin >> tc;
  while (tc--) solve();
  return 0;
}

```