#include <bits/stdc++.h>
using namespace std;
constexpr int bits(int x) { return x == 0 ? 0 : 31 - __builtin_clz(x); }
using ld = long double;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vd = vector<double>;
using vs = vector<string>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<double, double>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using vpdd = vector<pdd>;
template <typename T>
void ckmin(T &a, const T &b) {
  a = min(a, b);
}
template <typename T>
void ckmax(T &a, const T &b) {
  a = max(a, b);
}
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
namespace __input {
template <class T1, class T2>
void re(pair<T1, T2> &p);
template <class T>
void re(vector<T> &a);
template <class T, size_t SZ>
void re(array<T, SZ> &a);
template <class T>
void re(T &x) {
  cin >> x;
}
void re(double &x) {
  string t;
  re(t);
  x = stod(t);
}
template <class Arg, class... Args>
void re(Arg &first, Args &...rest) {
  re(first);
  re(rest...);
}
template <class T1, class T2>
void re(pair<T1, T2> &p) {
  re(p.f, p.s);
}
template <class T>
void re(vector<T> &a) {
  for (int i = 0; i < int((a).size()); i++) re(a[i]);
}
template <class T, size_t SZ>
void re(array<T, SZ> &a) {
  for (int i = 0; i < SZ; i++) re(a[i]);
}
}  // namespace __input
using namespace __input;
namespace __output {
template <typename T>
struct is_outputtable {
  template <typename C>
  static constexpr decltype(declval<ostream &>() << declval<const C &>(),
                            bool())
  test(int) {
    return true;
  }
  template <typename C>
  static constexpr bool test(...) {
    return false;
  }
  static constexpr bool value = test<T>(int());
};
template <
    class T, typename V = decltype(declval<const T &>().begin()),
    typename second = typename enable_if<!is_outputtable<T>::value, bool>::type>
void pr(const T &x);
template <class T,
          typename V = decltype(declval<ostream &>() << declval<const T &>())>
void pr(const T &x) {
  cout << x;
}
template <class T1, class T2>
void pr(const pair<T1, T2> &x);
template <class Arg, class... Args>
void pr(const Arg &first, const Args &...rest) {
  pr(first);
  pr(rest...);
}
template <class T, bool pretty = true>
void prContain(const T &x) {
  if (pretty) pr("{");
  bool fst = 1;
  for (const auto &a : x) pr(!fst ? pretty ? ", " : " " : "", a), fst = 0;
  if (pretty) pr("}");
}
template <class T>
void pc(const T &x) {
  prContain<T, false>(x);
  pr("\n");
}
template <class T1, class T2>
void pr(const pair<T1, T2> &x) {
  pr("{", x.f, ", ", x.s, "}");
}
template <class T, typename V, typename second>
void pr(const T &x) {
  prContain(x);
}
void ps() { pr("\n"); }
template <class Arg>
void ps(const Arg &first) {
  pr(first);
  ps();
}
template <class Arg, class... Args>
void ps(const Arg &first, const Args &...rest) {
  pr(first, " ");
  ps(rest...);
}
}  // namespace __output
using namespace __output;
namespace __algorithm {
template <typename T>
void dedup(vector<T> &v) {
  sort((v).begin(), (v).end());
  v.erase(unique((v).begin(), (v).end()), v.end());
}
template <typename T>
typename vector<T>::const_iterator find(const vector<T> &v, const T &x) {
  auto it = lower_bound((v).begin(), (v).end(), x);
  return it != v.end() && *it == x ? it : v.end();
}
template <typename T>
size_t index(const vector<T> &v, const T &x) {
  auto it = find(v, x);
  assert(it != v.end() && *it == x);
  return it - v.begin();
}
template <typename I>
struct _reversed_struct {
  I &v_;
  explicit _reversed_struct(I &v) : v_{v} {}
  typename I::reverse_iterator begin() const { return v_.rbegin(); }
  typename I::reverse_iterator end() const { return v_.rend(); }
};
template <typename I>
_reversed_struct<I> reversed(I &v) {
  return _reversed_struct<I>(v);
}
}  // namespace __algorithm
using namespace __algorithm;
namespace __io {
void setIO() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout << setprecision(15);
}
}  // namespace __io
using namespace __io;
template <typename T_vector>
void outvec(const T_vector &v, 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) << (i < end - 1 ? ' ' : '\n');
}
const ld pi = 3.14159265358979323846;
const ll mod = 1000000007;
const ll N = 7e5;
ll n, m, k, l, r, x, y, z;
const ll template_array_size = 1e6 + 1723;
ll ar[template_array_size];
ll br[template_array_size];
ll cr[template_array_size];
string s, t;
void solve() {
  int n, k;
  cin >> n >> k;
  vi a(n);
  re(a);
  for (int i = 0; i < n; i++) a[i]--;
  vector<vector<int>> dp(n + 1, vector<int>(n, (int)-1e9));
  dp[0][0] = 0;
  for (int i = 0; i < n; ++i) {
    for (int cnt = 0; cnt < n; ++cnt) {
      if (dp[i][cnt] < 0) continue;
      ckmax(dp[i + 1][cnt], dp[i][cnt] + (a[i] == i - cnt));
      if (cnt + 1 < n) {
        ckmax(dp[i + 1][cnt + 1], dp[i][cnt]);
      }
    }
  }
  int ans = n;
  for (int cnt = 0; cnt < n; ++cnt) {
    if (dp[n][cnt] >= k) {
      ckmin(ans, cnt);
    }
  }
  if (ans == n) ans = -1;
  cout << ans << endl;
}
int32_t main() {
  setIO();
  int t;
  cin >> t;
  for (int i = 0; i < t; i++) {
    solve();
  }
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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;
constexpr int bits(int x) { return x == 0 ? 0 : 31 - __builtin_clz(x); }
using ld = long double;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vd = vector<double>;
using vs = vector<string>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<double, double>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using vpdd = vector<pdd>;
template <typename T>
void ckmin(T &a, const T &b) {
  a = min(a, b);
}
template <typename T>
void ckmax(T &a, const T &b) {
  a = max(a, b);
}
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
namespace __input {
template <class T1, class T2>
void re(pair<T1, T2> &p);
template <class T>
void re(vector<T> &a);
template <class T, size_t SZ>
void re(array<T, SZ> &a);
template <class T>
void re(T &x) {
  cin >> x;
}
void re(double &x) {
  string t;
  re(t);
  x = stod(t);
}
template <class Arg, class... Args>
void re(Arg &first, Args &...rest) {
  re(first);
  re(rest...);
}
template <class T1, class T2>
void re(pair<T1, T2> &p) {
  re(p.f, p.s);
}
template <class T>
void re(vector<T> &a) {
  for (int i = 0; i < int((a).size()); i++) re(a[i]);
}
template <class T, size_t SZ>
void re(array<T, SZ> &a) {
  for (int i = 0; i < SZ; i++) re(a[i]);
}
}  // namespace __input
using namespace __input;
namespace __output {
template <typename T>
struct is_outputtable {
  template <typename C>
  static constexpr decltype(declval<ostream &>() << declval<const C &>(),
                            bool())
  test(int) {
    return true;
  }
  template <typename C>
  static constexpr bool test(...) {
    return false;
  }
  static constexpr bool value = test<T>(int());
};
template <
    class T, typename V = decltype(declval<const T &>().begin()),
    typename second = typename enable_if<!is_outputtable<T>::value, bool>::type>
void pr(const T &x);
template <class T,
          typename V = decltype(declval<ostream &>() << declval<const T &>())>
void pr(const T &x) {
  cout << x;
}
template <class T1, class T2>
void pr(const pair<T1, T2> &x);
template <class Arg, class... Args>
void pr(const Arg &first, const Args &...rest) {
  pr(first);
  pr(rest...);
}
template <class T, bool pretty = true>
void prContain(const T &x) {
  if (pretty) pr("{");
  bool fst = 1;
  for (const auto &a : x) pr(!fst ? pretty ? ", " : " " : "", a), fst = 0;
  if (pretty) pr("}");
}
template <class T>
void pc(const T &x) {
  prContain<T, false>(x);
  pr("\n");
}
template <class T1, class T2>
void pr(const pair<T1, T2> &x) {
  pr("{", x.f, ", ", x.s, "}");
}
template <class T, typename V, typename second>
void pr(const T &x) {
  prContain(x);
}
void ps() { pr("\n"); }
template <class Arg>
void ps(const Arg &first) {
  pr(first);
  ps();
}
template <class Arg, class... Args>
void ps(const Arg &first, const Args &...rest) {
  pr(first, " ");
  ps(rest...);
}
}  // namespace __output
using namespace __output;
namespace __algorithm {
template <typename T>
void dedup(vector<T> &v) {
  sort((v).begin(), (v).end());
  v.erase(unique((v).begin(), (v).end()), v.end());
}
template <typename T>
typename vector<T>::const_iterator find(const vector<T> &v, const T &x) {
  auto it = lower_bound((v).begin(), (v).end(), x);
  return it != v.end() && *it == x ? it : v.end();
}
template <typename T>
size_t index(const vector<T> &v, const T &x) {
  auto it = find(v, x);
  assert(it != v.end() && *it == x);
  return it - v.begin();
}
template <typename I>
struct _reversed_struct {
  I &v_;
  explicit _reversed_struct(I &v) : v_{v} {}
  typename I::reverse_iterator begin() const { return v_.rbegin(); }
  typename I::reverse_iterator end() const { return v_.rend(); }
};
template <typename I>
_reversed_struct<I> reversed(I &v) {
  return _reversed_struct<I>(v);
}
}  // namespace __algorithm
using namespace __algorithm;
namespace __io {
void setIO() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout << setprecision(15);
}
}  // namespace __io
using namespace __io;
template <typename T_vector>
void outvec(const T_vector &v, 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) << (i < end - 1 ? ' ' : '\n');
}
const ld pi = 3.14159265358979323846;
const ll mod = 1000000007;
const ll N = 7e5;
ll n, m, k, l, r, x, y, z;
const ll template_array_size = 1e6 + 1723;
ll ar[template_array_size];
ll br[template_array_size];
ll cr[template_array_size];
string s, t;
void solve() {
  int n, k;
  cin >> n >> k;
  vi a(n);
  re(a);
  for (int i = 0; i < n; i++) a[i]--;
  vector<vector<int>> dp(n + 1, vector<int>(n, (int)-1e9));
  dp[0][0] = 0;
  for (int i = 0; i < n; ++i) {
    for (int cnt = 0; cnt < n; ++cnt) {
      if (dp[i][cnt] < 0) continue;
      ckmax(dp[i + 1][cnt], dp[i][cnt] + (a[i] == i - cnt));
      if (cnt + 1 < n) {
        ckmax(dp[i + 1][cnt + 1], dp[i][cnt]);
      }
    }
  }
  int ans = n;
  for (int cnt = 0; cnt < n; ++cnt) {
    if (dp[n][cnt] >= k) {
      ckmin(ans, cnt);
    }
  }
  if (ans == n) ans = -1;
  cout << ans << endl;
}
int32_t main() {
  setIO();
  int t;
  cin >> t;
  for (int i = 0; i < t; i++) {
    solve();
  }
  return 0;
}

```