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.*;
  import java.util.*;
  
  public class PermutationShift implements Runnable {
  
      void solve() {
          int t = ri();
          while (t-- > 0) {
              int n = ri(), m = ri();
              int[] perm = iArr(n);
              for (int i = 0; i < n; i++) {
                  perm[i] = ri() - 1;
              }
              int[] count = iArr(n);
              for (int i = 0; i < n; i++) {
                  count[(i + n - perm[i]) % n]++;
              }
  
              List<Integer> ans = new ArrayList<Integer>();
              for (int i = 0; i < n; i++) {
                  if (count[i] + 2 * m >= n && check(n, m, i, perm)) {
                      ans.add(i);
                  }
              }
              print(ans.size() + " ");
              ans.forEach(o -> print(o + " "));
              println("");
          }
      }
  
      boolean check(int n, int m, int k, int[] perm) {
          DSU o = new DSU(n);
          for (int i = 0; i < n; i++) {
              o.unite(((i + n - k) % n), perm[i]);
          }
          return (n - o.totalDistinct) <= m;
      }
  
      static class DSU {
          int[] parent;
          int[] size;
          int totalDistinct;
  
          public DSU(int n) {
              size = new int[n + 1];
              parent = new int[n + 1];
              Arrays.fill(parent, -1);
              Arrays.fill(size, 1);
              totalDistinct = n;
          }
  
          public boolean unite(int a, int b) {
              a = find(a);
              b = find(b);
              if (a == b) {
                  return false;
              }
              if (size[a] < size[b]) {
                  a = a ^ b ^ (b = a);
              }
              parent[b] = a;
              size[a] += size[b];
              size[b] = 0;
              totalDistinct--;
              return true;
          }
  
          private int find(int num) {
              return (parent[num] == -1) ? num : (parent[num] = find(parent[num]));
          }
  
      }
  
      /************************************************************************************************************************************************/
      public static void main(String[] args) throws IOException {
          new Thread(null, new PermutationShift(), "1").start();
      }
  
      static PrintWriter out = new PrintWriter(System.out);
      static Reader read = new Reader();
      static StringBuilder sbr = new StringBuilder();
      static int mod = (int) 1e9 + 7;
      static int dmax = Integer.MAX_VALUE;
      static long lmax = Long.MAX_VALUE;
      static int dmin = Integer.MIN_VALUE;
      static long lmin = Long.MIN_VALUE;
      static int[] dprimes = new int[]{1, 11, 101, 1087, 99991, 100001, 1000003, 15485863, 999999937};
  
      @Override
      public void run() {
          solve();
          out.close();
      }
  
      static class Reader {
          private byte[] buf = new byte[1024];
          private int index;
          private InputStream in;
          private int total;
  
          public Reader() {
              in = System.in;
          }
  
          public int scan() throws IOException {
              if (total < 0)
                  throw new InputMismatchException();
              if (index >= total) {
                  index = 0;
                  total = in.read(buf);
                  if (total <= 0)
                      return -1;
              }
              return buf[index++];
          }
  
          public int intNext() throws IOException {
              int integer = 0;
              int n = scan();
              while (isWhiteSpace(n))
                  n = scan();
              int neg = 1;
              if (n == '-') {
                  neg = -1;
                  n = scan();
              }
              while (!isWhiteSpace(n)) {
                  if (n >= '0' && n <= '9') {
                      integer *= 10;
                      integer += n - '0';
                      n = scan();
                  } else
                      throw new InputMismatchException();
              }
              return neg * integer;
          }
  
          public double doubleNext() throws IOException {
              double doub = 0;
              int n = scan();
              while (isWhiteSpace(n))
                  n = scan();
              int neg = 1;
              if (n == '-') {
                  neg = -1;
                  n = scan();
              }
              while (!isWhiteSpace(n) && n != '.') {
                  if (n >= '0' && n <= '9') {
                      doub *= 10;
                      doub += n - '0';
                      n = scan();
                  } else
                      throw new InputMismatchException();
              }
              if (n == '.') {
                  n = scan();
                  double temp = 1;
                  while (!isWhiteSpace(n)) {
                      if (n >= '0' && n <= '9') {
                          temp /= 10;
                          doub += (n - '0') * temp;
                          n = scan();
                      } else
                          throw new InputMismatchException();
                  }
              }
              return doub * neg;
          }
  
          public String read() throws IOException {
              StringBuilder sb = new StringBuilder();
              int n = scan();
              while (isWhiteSpace(n))
                  n = scan();
              while (!isWhiteSpace(n)) {
                  sb.append((char) n);
                  n = scan();
              }
              return sb.toString();
          }
  
          public String rline() throws IOException {
              StringBuilder sb = new StringBuilder();
              int n = scan();
              while (n != '\n') {
                  sb.append((char) n);
                  n = scan();
              }
              return sb.toString();
          }
  
          private boolean isWhiteSpace(int n) {
              if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1)
                  return true;
              return false;
          }
      }
  
      static void print(Object object) {
          out.print(object);
      }
  
      static void println(Object object) {
          out.println(object);
      }
  
      static int[] iArr(int len) {
          return new int[len];
      }
  
      static long[] lArr(int len) {
          return new long[len];
      }
  
      static long min(long a, long b) {
          return Math.min(a, b);
      }
  
      static int min(int a, int b) {
          return Math.min(a, b);
      }
  
      static long max(Long a, Long b) {
          return Math.max(a, b);
      }
  
      static int max(int a, int b) {
          return Math.max(a, b);
      }
  
      static int ri() {
          try {
              return read.intNext();
          } catch (IOException e) {
              e.printStackTrace();
          }
          System.exit(2);
          return -1;
      }
  
      static long rl() {
          try {
              return Long.parseLong(read.read());
          } catch (IOException e) {
              e.printStackTrace();
          }
          System.exit(2);
          return -1;
      }
  
      static String rs() {
          try {
              return read.read();
          } catch (IOException e) {
              e.printStackTrace();
          }
          System.exit(2);
          return "";
      }
  
      static String rline() {
          try {
              return read.rline();
          } catch (IOException e) {
              e.printStackTrace();
          }
          System.exit(2);
          return "";
      }
  
      static char rc() {
          return rs().charAt(0);
      }
  
      static double rd() {
          try {
              return read.doubleNext();
          } catch (IOException e) {
              e.printStackTrace();
          }
          System.exit(2);
          return -1;
      }
  }
  