#include <bits/stdc++.h>
using namespace std;
using ll = long long;
ll MODULO_007 = 1000000007;
ll MODULO_009 = 1000000009;
ll MOD = MODULO_007;
int main() {
  ios::sync_with_stdio(false);
  int T;
  cin >> T;
  for (int t = 0; t < T; t++) {
    int N;
    cin >> N;
    int posOp;
    cin >> posOp;
    vector<int> arr(N);
    vector<int> pos(N);
    for (int i = 0; i < N; i++) {
      cin >> arr[i];
      pos[arr[i] - 1] = i;
    }
    vector<int> shiftNeeded(N);
    for (int i = 0; i < N; i++) {
      shiftNeeded[i] = pos[i] - i;
      shiftNeeded[i] = (shiftNeeded[i] + N) % N;
    }
    vector<int> votesForShifts(N, 0);
    {
      for (int e : shiftNeeded) {
        votesForShifts[e]++;
      }
    }
    vector<int> resultingKs;
    for (int i = 0; i < N; i++) {
      if (votesForShifts[i] + 2 * posOp >= N) {
        vector<int> aftershifted(N);
        vector<int> reference(N);
        for (int j = 0; j < N; j++) {
          aftershifted[j] = ((j + N - i) % N);
          reference[j] = arr[j] - 1;
        }
        vector<pair<int, int>> vec(N, pair<int, int>(-1, -1));
        for (int j = 0; j < N; j++) {
          vec[aftershifted[j]].first = j;
          vec[reference[j]].second = j;
        }
        int needOps = 0;
        vector<bool> visited(N + 5, false);
        vector<vector<int>> neis(N + 5);
        for (int j = 0; j < N; j++) {
          if (vec[j].first == vec[j].second) continue;
          neis[vec[j].first].push_back(vec[j].second);
          neis[vec[j].second].push_back(vec[j].first);
        }
        for (int j = 0; j < N; j++) {
          if (visited[j]) {
            continue;
          }
          int compSize = 0;
          queue<int> q;
          q.push(j);
          while (!q.empty()) {
            int cur = q.front();
            q.pop();
            if (visited[cur]) {
              continue;
            }
            visited[cur] = true;
            compSize += 1;
            for (int a : neis[cur]) {
              if (visited[a]) {
                continue;
              }
              q.push(a);
            }
          }
          if (compSize > 1) {
            needOps += compSize - 1;
          }
        }
        if (needOps <= posOp) {
          resultingKs.push_back(i);
        }
      }
    }
    cout << resultingKs.size() << " ";
    sort(resultingKs.begin(), resultingKs.end());
    for (int e : resultingKs) {
      cout << e << " ";
    }
    cout << endl;
  }
  return 0;
}

### Prompt

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

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;
using ll = long long;
ll MODULO_007 = 1000000007;
ll MODULO_009 = 1000000009;
ll MOD = MODULO_007;
int main() {
  ios::sync_with_stdio(false);
  int T;
  cin >> T;
  for (int t = 0; t < T; t++) {
    int N;
    cin >> N;
    int posOp;
    cin >> posOp;
    vector<int> arr(N);
    vector<int> pos(N);
    for (int i = 0; i < N; i++) {
      cin >> arr[i];
      pos[arr[i] - 1] = i;
    }
    vector<int> shiftNeeded(N);
    for (int i = 0; i < N; i++) {
      shiftNeeded[i] = pos[i] - i;
      shiftNeeded[i] = (shiftNeeded[i] + N) % N;
    }
    vector<int> votesForShifts(N, 0);
    {
      for (int e : shiftNeeded) {
        votesForShifts[e]++;
      }
    }
    vector<int> resultingKs;
    for (int i = 0; i < N; i++) {
      if (votesForShifts[i] + 2 * posOp >= N) {
        vector<int> aftershifted(N);
        vector<int> reference(N);
        for (int j = 0; j < N; j++) {
          aftershifted[j] = ((j + N - i) % N);
          reference[j] = arr[j] - 1;
        }
        vector<pair<int, int>> vec(N, pair<int, int>(-1, -1));
        for (int j = 0; j < N; j++) {
          vec[aftershifted[j]].first = j;
          vec[reference[j]].second = j;
        }
        int needOps = 0;
        vector<bool> visited(N + 5, false);
        vector<vector<int>> neis(N + 5);
        for (int j = 0; j < N; j++) {
          if (vec[j].first == vec[j].second) continue;
          neis[vec[j].first].push_back(vec[j].second);
          neis[vec[j].second].push_back(vec[j].first);
        }
        for (int j = 0; j < N; j++) {
          if (visited[j]) {
            continue;
          }
          int compSize = 0;
          queue<int> q;
          q.push(j);
          while (!q.empty()) {
            int cur = q.front();
            q.pop();
            if (visited[cur]) {
              continue;
            }
            visited[cur] = true;
            compSize += 1;
            for (int a : neis[cur]) {
              if (visited[a]) {
                continue;
              }
              q.push(a);
            }
          }
          if (compSize > 1) {
            needOps += compSize - 1;
          }
        }
        if (needOps <= posOp) {
          resultingKs.push_back(i);
        }
      }
    }
    cout << resultingKs.size() << " ";
    sort(resultingKs.begin(), resultingKs.end());
    for (int e : resultingKs) {
      cout << e << " ";
    }
    cout << endl;
  }
  return 0;
}

```