description: 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]. 
solution: import java.io.IOException;
  import java.io.InputStream;
  import java.io.OutputStream;
  import java.io.PrintWriter;
  import java.util.ArrayList;
  import java.util.InputMismatchException;
  import java.util.List;
  
  public class TaskE {
  
    static class Solver implements Runnable {
  
      int t, n, m;
      int[] perm, cnt;
      InputReader in;
      PrintWriter out;
  
      void solve() throws IOException {
        t = in.nextInt();
  
        while (t-- > 0) {
          n = in.nextInt();
          m = in.nextInt();
          perm = new int[n];
          cnt = new int[n];
  
          for (int i = 0; i < n; i++) {
            int x = in.nextInt() - 1;
            int k = i - x;
  
            perm[i] = x;
  
            if (k < 0) {
              k += n;
            }
  
            cnt[k]++;
          }
  
          List<Integer> ans = new ArrayList<>();
  
          for (int i = 0; i < n; i++) {
            if (cnt[i] >= n / 3) {
              if (check(i)) {
                ans.add(i);
              }
            }
          }
  
          out.print(ans.size()  + " ");
  
          for (int x : ans) {
            out.print(x + " ");
          }
  
          out.println();
        }
      }
  
      boolean check(int k) {
        List<Integer>[] adj = new List[n];
        boolean[] vis = new boolean[n];
  
        for (int i = 0; i < n; i++) {
          adj[i] = new ArrayList<>();
        }
  
        for (int i = 0; i < n; i++) {
          int p = perm[i];
          int iNew = (p + k) % n;
  
          if (i != iNew) {
            adj[i].add(iNew);
            adj[iNew].add(i);
          }
        }
  
        int size = 0;
        int components = 0;
  
        for (int i = 0; i < n; i++) {
          if (!vis[i]) {
            size += dfs(i, adj, vis);
            components++;
          }
        }
  
        return size - components <= m;
      }
  
      int dfs(int curr, List<Integer>[] adj, boolean[] vis) {
        vis[curr] = true;
  
        int size = 1;
  
        for (int next : adj[curr]) {
          if (!vis[next]) {
            size += dfs(next, adj, vis);
          }
        }
  
        return size;
      }
  
      public Solver(InputReader in, PrintWriter out) {
        this.in = in;
        this.out = out;
      }
  
      @Override
      public void run() {
        try {
          solve();
        } catch (IOException e) {
          e.printStackTrace();
        }
      }
  
    }
  
    static class InputReader {
  
      private InputStream stream;
      private byte[] buf = new byte[1024];
      private int curChar;
      private int numChars;
  
      public int read() {
          if (numChars == -1) {
              throw new InputMismatchException();
          }
  
        if (curChar >= numChars) {
          curChar = 0;
          try {
            numChars = stream.read(buf);
          } catch (IOException e) {
            throw new InputMismatchException();
          }
            if (numChars <= 0) {
                return -1;
            }
        }
  
        return buf[curChar++];
      }
  
      public int nextInt() {
        int c = read();
  
          while (isSpaceChar(c)) {
              c = read();
          }
  
        int sgn = 1;
  
        if (c == '-') {
          sgn = -1;
          c = read();
        }
  
        int res = 0;
  
        do {
            if (c < '0' || c > '9') {
                throw new InputMismatchException();
            }
  
          res *= 10;
          res += c & 15;
  
          c = read();
        } while (!isSpaceChar(c));
  
        return res * sgn;
      }
  
      public int[] nextIntArray(int arraySize) {
        int array[] = new int[arraySize];
  
          for (int i = 0; i < arraySize; i++) {
              array[i] = nextInt();
          }
  
        return array;
      }
  
      public long nextLong() {
        int c = read();
  
          while (isSpaceChar(c)) {
              c = read();
          }
  
        int sign = 1;
  
        if (c == '-') {
          sign = -1;
  
          c = read();
        }
  
        long result = 0;
  
        do {
            if (c < '0' || c > '9') {
                throw new InputMismatchException();
            }
  
          result *= 10;
          result += c & 15;
  
          c = read();
        } while (!isSpaceChar(c));
  
        return result * sign;
      }
  
      public long[] nextLongArray(int arraySize) {
        long array[] = new long[arraySize];
  
          for (int i = 0; i < arraySize; i++) {
              array[i] = nextLong();
          }
  
        return array;
      }
  
      public float nextFloat() {
        float result, div;
        byte c;
  
        result = 0;
        div = 1;
        c = (byte) read();
  
          while (c <= ' ') {
              c = (byte) read();
          }
  
        boolean isNegative = (c == '-');
  
          if (isNegative) {
              c = (byte) read();
          }
  
        do {
          result = result * 10 + c - '0';
        } while ((c = (byte) read()) >= '0' && c <= '9');
  
          if (c == '.') {
              while ((c = (byte) read()) >= '0' && c <= '9') {
                  result += (c - '0') / (div *= 10);
              }
          }
  
          if (isNegative) {
              return -result;
          }
  
        return result;
      }
  
      public double nextDouble() {
        double ret = 0, div = 1;
        byte c = (byte) read();
  
          while (c <= ' ') {
              c = (byte) read();
          }
  
        boolean neg = (c == '-');
  
          if (neg) {
              c = (byte) read();
          }
  
        do {
          ret = ret * 10 + c - '0';
        } while ((c = (byte) read()) >= '0' && c <= '9');
  
          if (c == '.') {
              while ((c = (byte) read()) >= '0' && c <= '9') {
                  ret += (c - '0') / (div *= 10);
              }
          }
  
          if (neg) {
              return -ret;
          }
  
        return ret;
      }
  
      public String next() {
        int c = read();
  
          while (isSpaceChar(c)) {
              c = read();
          }
  
        StringBuilder res = new StringBuilder();
  
        do {
          res.appendCodePoint(c);
  
          c = read();
        } while (!isSpaceChar(c));
  
        return res.toString();
      }
  
      public boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
      }
  
      public String nextLine() {
        int c = read();
  
        StringBuilder result = new StringBuilder();
  
        do {
          result.appendCodePoint(c);
  
          c = read();
        } while (!isNewLine(c));
  
        return result.toString();
      }
  
      public boolean isNewLine(int c) {
        return c == '\n';
      }
  
      public void close() {
        try {
          stream.close();
        } catch (IOException e) {
          e.printStackTrace();
        }
      }
  
      public InputReader(InputStream stream) {
        this.stream = stream;
      }
  
    }
  
    TaskE(InputStream inputStream, OutputStream outputStream) {
      InputReader in = new InputReader(inputStream);
      PrintWriter out = new PrintWriter(outputStream);
      Thread thread = new Thread(null, new Solver(in, out), "Solver", 1 << 29);
  
      try {
        thread.start();
        thread.join();
      } catch (InterruptedException e) {
        e.printStackTrace();
      } finally {
        in.close();
        out.flush();
        out.close();
      }
    }
  
    public static void main(String[] args) {
      new TaskE(System.in, System.out);
    }
  
  }
  