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]. 
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);
  }

}
