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.util.*;
  import java.io.*;
  import static java.lang.Math.min;
  import static java.lang.Math.abs;
  import static java.lang.Math.max;
  public class EdE {
  	static long[] mods = {1000000007, 998244353, 1000000009};
  	static long mod = mods[0];
  	public static MyScanner sc;
      public static PrintWriter out;
  	public static void main(String[] largewang) throws Exception{
  		// TODO Auto-generated method stub
   		sc = new MyScanner();
   		out = new PrintWriter(System.out);
   		int t = sc.nextInt();
   		while (t-->0) {
   			int n = sc.nextInt();
   			int m = sc.nextInt();
   			int[] arr = readArrayInt1(n);
   			int[] dist = new int[n+1];
   			for(int j = 1;j<=n;j++){
   				dist[arr[j]] = ((j - arr[j])%n+n)%n;
   			}
   			int[] freq = new int[n];
   			for(int j =1;j<=n;j++){
   				freq[dist[j]]++;
   			}
   			ArrayList<Integer> poss = new ArrayList<>();
   			for(int j = 0;j<n;j++){
   				if (freq[j]*3 >= n) {
   					poss.add(j);
   				}
   			}
   			ArrayList<Integer> ans = new ArrayList<>();
   			for(int j : poss) {
  	 			if (works(j, m, arr)) {
  	 				ans.add(j);
  	 			}
   			}
   			out.print(ans.size() + " ");
   			for(int j : ans) {
   				out.print(j + " ");
   			}
   			out.println();
   		}
   		out.close();
   		
   	}
  	public static boolean works (int j, int m, int[] input) {
  		int n = input.length-1;
  		int[] arr = new int[n+1];
  		int count = 0;
  		for(int k = j+1;k<=n;k++){
  			arr[k] = k-j;
  			count++;
  		}
  		for(int k = 1;k<=j;k++){
  			arr[k] = count + k;
  		}
  		int[] pos = new int[n+1];
  		
  		for(int k = 1;k<=n;k++){
  			pos[arr[k]] = k;
  		}
  		int cycles =0 ;
  		Set<Integer> seen = new HashSet<>();
  		ArrayDeque<Integer> q = new ArrayDeque<>();
  		int[] adj = new int[n+1];
  		for(int k = 1;k<=n;k++){
  			adj[k] = pos[input[k]];
  		}
  		for(int k = 1;k<=n;k++){
  			if (arr[k] != input[k] && !seen.contains(k)){
  				cycles++;
  				seen.add(k);
  				q.add(k);
  				while(!q.isEmpty()) {
  					int v = q.remove();
  					if (!seen.contains(adj[v])) {
  						seen.add(adj[v]);
  						q.add(adj[v]);
  					}
  				}
  			}
  		}
  		return seen.size() - cycles <= m;
  		
  	}
  	
  	public static void sort(int[] array){
  		ArrayList<Integer> copy = new ArrayList<>();
  		for (int i : array)
  			copy.add(i);
  		Collections.sort(copy);
  		for(int i = 0;i<array.length;i++)
  			array[i] = copy.get(i);
  	}
  	static String[] readArrayString(int n){
  		String[] array = new String[n];
  		for(int j =0 ;j<n;j++)
  			array[j] = sc.next();
  		return array;
  	}
  	static int[] readArrayInt(int n){
      	int[] array = new int[n];
      	for(int j = 0;j<n;j++)
      		array[j] = sc.nextInt();
      	return array;
      }
  	static int[] readArrayInt1(int n){
  		int[] array = new int[n+1];
  		for(int j = 1;j<=n;j++){
  			array[j] = sc.nextInt();
  		}
  		return array;
  	}
  	static long[] readArrayLong(int n){
  		long[] array = new long[n];
  		for(int j =0 ;j<n;j++)
  			array[j] = sc.nextLong();
  		return array;
  	}
  	static double[] readArrayDouble(int n){
  		double[] array = new double[n];
  		for(int j =0 ;j<n;j++)
  			array[j] = sc.nextDouble();
  		return array;
  	}
  	static int minIndex(int[] array){
  		int minValue = Integer.MAX_VALUE;
  		int minIndex = -1;
  		for(int j = 0;j<array.length;j++){
  			if (array[j] < minValue){
  				minValue = array[j];
  				minIndex = j;
  			}
  		}
  		return minIndex;
  	}
  	static int minIndex(long[] array){
  		long minValue = Long.MAX_VALUE;
  		int minIndex = -1;
  		for(int j = 0;j<array.length;j++){
  			if (array[j] < minValue){
  				minValue = array[j];
  				minIndex = j;
  			}
  		}
  		return minIndex;
  	}
  	static int minIndex(double[] array){
  		double minValue = Double.MAX_VALUE;
  		int minIndex = -1;
  		for(int j = 0;j<array.length;j++){
  			if (array[j] < minValue){
  				minValue = array[j];
  				minIndex = j;
  			}
  		}
  		return minIndex;
  	}
  	static long power(long x, long y){
  		if (y == 0)
  			return 1;
  		if (y%2 == 1)
  			return (x*power(x, y-1))%mod;
  		return power((x*x)%mod, y/2)%mod;
  	}
  	static void verdict(boolean a){
          out.println(a ? "YES" : "NO");
      }
      public static class MyScanner {
          BufferedReader br;
          StringTokenizer st;
          public MyScanner() {
              br = new BufferedReader(new InputStreamReader(System.in));
          }
          String next() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } 
                  catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
          int nextInt() {
              return Integer.parseInt(next());
          }
          long nextLong() {
              return Long.parseLong(next());
          }
          double nextDouble() {
              return Double.parseDouble(next());
          }
          String nextLine() {
              String str = "";
              try{
                  str = br.readLine();
              } 
              catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
          
      }	
  }
  
  //StringJoiner sj = new StringJoiner(" "); 
  //sj.add(strings)
  //sj.toString() gives string of those stuff w spaces or whatever that sequence is