#include <bits/stdc++.h>
using namespace std;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
void debug3(int *t, int st, int n) {
  cerr << '{' << t[st];
  for (int i = st + 1; i <= n; i++) cerr << ",", __print(t[i]);
  cerr << "}" << '\n';
}
const int MOD = 1e9 + 7;
int v[300005], a[300005], b[300005];
map<int, int> mp;
set<int> sol;
set<int> s;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t, n, m, i, ct, op;
  cin >> t;
  while (t--) {
    cin >> n >> m;
    mp.clear();
    sol.clear();
    for (i = 1; i <= n; i++) cin >> v[i];
    for (i = 1; i <= n; i++) a[i] = (v[i] - i + n) % n;
    for (i = 1; i <= n; i++) mp[a[i]]++;
    for (auto vec : mp) {
      if (n - vec.second > 2 * m) continue;
      if (n - vec.second <= m + 1)
        sol.insert((n - vec.first) % n);
      else {
        for (i = 1; i <= n; i++) b[(i + vec.first - 1) % n + 1] = v[i];
        ct = 0;
        op = 0;
        for (i = 1; i <= n; i++) {
          if (b[i] != i) {
            ct++;
            swap(b[i], b[b[i]]);
            i--;
          }
        }
        if (ct <= m) {
          sol.insert((n - vec.first) % n);
        }
      }
    }
    cout << sol.size() << " ";
    for (auto vec : sol) cout << vec << " ";
    cout << '\n';
  }
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

An identity permutation of length n is an array [1, 2, 3, ..., n].

We performed the following operations to an identity permutation of length n:

  * firstly, we cyclically shifted it to the right by k positions, where k is unknown to you (the only thing you know is that 0 ≤ k ≤ n - 1). When an array is cyclically shifted to the right by k positions, the resulting array is formed by taking k last elements of the original array (without changing their relative order), and then appending n - k first elements to the right of them (without changing relative order of the first n - k elements as well). For example, if we cyclically shift the identity permutation of length 6 by 2 positions, we get the array [5, 6, 1, 2, 3, 4]; 
  * secondly, we performed the following operation at most m times: pick any two elements of the array and swap them. 



You are given the values of n and m, and the resulting array. Your task is to find all possible values of k in the cyclic shift operation.

Input

The first line contains one integer t (1 ≤ t ≤ 10^5) — the number of test cases.

Each test case consists of two lines. The first line contains two integers n and m (3 ≤ n ≤ 3 ⋅ 10^5; 0 ≤ m ≤ n/3).

The second line contains n integers p_1, p_2, ..., p_n (1 ≤ p_i ≤ n, each integer from 1 to n appears in this sequence exactly once) — the resulting array.

The sum of n over all test cases does not exceed 3 ⋅ 10^5.

Output

For each test case, print the answer in the following way:

  * firstly, print one integer r (0 ≤ r ≤ n) — the number of possible values of k for the cyclic shift operation; 
  * secondly, print r integers k_1, k_2, ..., k_r (0 ≤ k_i ≤ n - 1) — all possible values of k in increasing order. 

Example

Input


4
4 1
2 3 1 4
3 1
1 2 3
3 1
3 2 1
6 0
1 2 3 4 6 5


Output


1 3
1 0
3 0 1 2
0

Note

Consider the example: 

  * in the first test case, the only possible value for the cyclic shift is 3. If we shift [1, 2, 3, 4] by 3 positions, we get [2, 3, 4, 1]. Then we can swap the 3-rd and the 4-th elements to get the array [2, 3, 1, 4]; 
  * in the second test case, the only possible value for the cyclic shift is 0. If we shift [1, 2, 3] by 0 positions, we get [1, 2, 3]. Then we don't change the array at all (we stated that we made at most 1 swap), so the resulting array stays [1, 2, 3]; 
  * in the third test case, all values from 0 to 2 are possible for the cyclic shift: 
    * if we shift [1, 2, 3] by 0 positions, we get [1, 2, 3]. Then we can swap the 1-st and the 3-rd elements to get [3, 2, 1]; 
    * if we shift [1, 2, 3] by 1 position, we get [3, 1, 2]. Then we can swap the 2-nd and the 3-rd elements to get [3, 2, 1]; 
    * if we shift [1, 2, 3] by 2 positions, we get [2, 3, 1]. Then we can swap the 1-st and the 2-nd elements to get [3, 2, 1]; 
  * in the fourth test case, we stated that we didn't do any swaps after the cyclic shift, but no value of cyclic shift could produce the array [1, 2, 3, 4, 6, 5]. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
void debug3(int *t, int st, int n) {
  cerr << '{' << t[st];
  for (int i = st + 1; i <= n; i++) cerr << ",", __print(t[i]);
  cerr << "}" << '\n';
}
const int MOD = 1e9 + 7;
int v[300005], a[300005], b[300005];
map<int, int> mp;
set<int> sol;
set<int> s;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t, n, m, i, ct, op;
  cin >> t;
  while (t--) {
    cin >> n >> m;
    mp.clear();
    sol.clear();
    for (i = 1; i <= n; i++) cin >> v[i];
    for (i = 1; i <= n; i++) a[i] = (v[i] - i + n) % n;
    for (i = 1; i <= n; i++) mp[a[i]]++;
    for (auto vec : mp) {
      if (n - vec.second > 2 * m) continue;
      if (n - vec.second <= m + 1)
        sol.insert((n - vec.first) % n);
      else {
        for (i = 1; i <= n; i++) b[(i + vec.first - 1) % n + 1] = v[i];
        ct = 0;
        op = 0;
        for (i = 1; i <= n; i++) {
          if (b[i] != i) {
            ct++;
            swap(b[i], b[b[i]]);
            i--;
          }
        }
        if (ct <= m) {
          sol.insert((n - vec.first) % n);
        }
      }
    }
    cout << sol.size() << " ";
    for (auto vec : sol) cout << vec << " ";
    cout << '\n';
  }
}

```