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]. 
			/*
			TO LEARN
			1-segment trees
			2-euler tour
		
			*/
			/*
			TO SOLVE 
			uva 1103
			codeforces 722 kavi on pairing duty
			*/
			/*
			bit manipulation shit
			1-Computer Systems: A Programmer's Perspective
			2-hacker's delight
			3-(02-03-bits-ints)
			4-machine-basics
			5-Bits Manipulation tutorialspoint
			*/
			/*
			TO WATCH
			1-what is bitmasking by kartik arora youtube
			*/
			            import java.util.*;
					    import java.math.*;
					    import java.io.*; 
					    import java.util.stream.Collectors;

					       public class A{
					     
					  static InputStream inputStream = System.in;
			            static FastScanner scan=new FastScanner();
					     public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	static int n;
	static int check(int arr1[],int arr2[])
	{
		int pos[]=new int[n];
		for(int i=0;i<n;i++)
			pos[arr1[i]]=i;
		int edges[]=new int[n];
		for(int i=0;i<n;i++)
		{
			edges[pos[arr2[i]]]=i;
		}
		boolean vis[]=new boolean[n];
		int res=0;
		for(int i=0;i<n;i++)
		{
			int k=i;
			int size=0;
			if(!vis[k]){
			while(!vis[k])
			{
				//out.println("FUCK");
				size++;
				vis[k]=true;
				k=edges[k];

			}


			if(k==i){
		//out.println("FUCK");
			res+=(size-1);
		}}
		}
		return res;
	}
	static int [] RightRotate(int a[], int k)
{
     
    // If rotation is greater
    // than size of array
    k = k % n;
 int tmp[]=new int[n];
    for(int i = 0; i < n; i++)
    {
       if(i < k)
       {
            
           // Printing rightmost
           // kth elements
          tmp[i]=a[n + i - k];
       }
       else
       {
            
           
           tmp[i]=a[i - k];
       }
    }
    return tmp;
}



				public static void main(String[] args)  throws Exception 
			      {
				
						///scan=new FastScanner("cownomics.in");
					//out = new PrintWriter("cownomics.out");
					 
					 /*
					 currently doing 
					 1-digit dp
					 2-ds like fenwick and interval tree and sparse table 
					 */
					 /*
					 READING 
					 1-Everything About Dynamic Programming codeforces
					 2-DYNAMIC PROGRAMMING: FROM NOVICE TO ADVANCED topcoder
					 3-Introduction to DP with Bitmasking codefoces
					 4-Bit Manipulation hackerearth
					 5-read more about mobious and inculsion-exclusion 
					 */
		



					    int tt=1;
					tt=scan.nextInt();
					int T=tt;
					/*Map<Integer,Pair>map=new HashMap<Integer,Pair>();
					for(int i=1;i<=333333334;i++)
					{
						map.put(i+2*i,new Pair(i,2*i));
						map.put(i+(2*(i+1)),new Pair(i,i+1));
						map.put(i+1+(2*i),new Pair(i+1,i));
					}*/

				 outer:while(tt-->0)
					    {
				n=scan.nextInt();
				int m=scan.nextInt();
				int arr[]=new int[n];
				int pos[]=new int[n];

				for(int i=0;i<n;i++)
				{
					arr[i]=scan.nextInt()-1;
					pos[arr[i]]=i;
				}
				int orig[]=new int[n];
				for(int i=0;i<n;i++){
					orig[i]=i;

				}
				int cnt[]=new int[n];

				for(int i=0;i<n;i++)
				{
					int p=pos[i];
					if(p>i)
					{
						cnt[p-i]++;
					}
					else if(p<i)
					{
						int to=n-p-1;
						to+=p;
						cnt[to]++;
					}
				}
				//out.println(cnt[2]);
				ArrayList<Integer>res=new ArrayList<Integer>();
				if(check(orig,arr)<=m)
					res.add(0);
				for(int i=0;i<n;i++)
				{
					if(cnt[i]+100>=n/3){
						//out.println("FUCK");
					int tmp[]=RightRotate(orig,i+1);
					//if(i+1==3)
					//	out.println(Arrays.toString(tmp));
					if(check(tmp,arr)<=m&&i+1!=n)
						res.add(i+1);
				}
				}
				if(tt==50001- 64339)
					out.println("FUCK "+res.size());
				out.println(res.size());
				for(int r:res)
					out.print(r+" ");

				out.println();
					    

					   

					   
					    	
					    	
			}
			   out.close();
		}
		  	 
			 		  
					   
					
					static class special{
						boolean bool;
						int n;
						//int id;
						special(boolean bool,int n)
						{
							this.bool=bool;
							this.n=n;
						}
						@Override
						    public int hashCode() {
					                int hash = 7;
		    hash = 31 * hash + (int) n;
		   
		    return hash;
					            }
					              @Override
					            public boolean equals(Object o){
					                if (o == this) return true;
					                if (o.getClass() != getClass()) return false;
					                special t = (special)o;
					                return t.bool == bool && t.n == n;
					            }
					}

					   
					     static long binexp(long a,long n)
					    {
					        if(n==0)
					            return 1;
					        long res=binexp(a,n/2);
					        if(n%2==1)
					            return res*res*a;
					        else 
					            return res*res;
					    }
					     
					    static long powMod(long base, long exp, long mod) {
					           if (base == 0 || base == 1) return base;
					           if (exp == 0) return 1;
					           if (exp == 1) return (base % mod+mod)%mod;
					           long R = (powMod(base, exp/2, mod) % mod+mod)%mod;
					           R *= R;
					           R %= mod;
					           if ((exp & 1) == 1) {
					               return (base * R % mod+mod)%mod;
					           }
					           else return (R %mod+mod)%mod;
					       }
					    static double dis(double x1,double y1,double x2,double y2)
					    {
					        return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
					    }
					    static long mod(long x,long y)
					        {
					            if(x<0)
					                x=x+(-x/y+1)*y;
					            return x%y;
					        }
					     public static  long pow(long b, long e) {
					                long r = 1;
					                while (e > 0) {
					                    if (e % 2 == 1) r = r * b ;
					                    b = b * b;
					                    e >>= 1;
					                }
					                return r;
					            }
					    private static void sort(long[] arr) {
					            List<Long> list = new ArrayList<>();
					            for (long object : arr) list.add(object);
					            Collections.sort(list);
					        //Collections.reverse(list);
					            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
					        }
					    private static void sort2(long[] arr) {
					            List<Long> list = new ArrayList<>();
					            for (Long object : arr) list.add(object);
					            Collections.sort(list);
					        Collections.reverse(list);
					            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
					        }
					     static class FastScanner
			{
			    private int BS = 1 << 16;
			    private char NC = (char) 0;
			    private byte[] buf = new byte[BS];
			    private int bId = 0, size = 0;
			    private char c = NC;
			    private double cnt = 1;
			    private BufferedInputStream in;
			 
			    public FastScanner() {
			        in = new BufferedInputStream(System.in, BS);
			    }
			 
			    public FastScanner(String s) {
			        try {
			            in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
			        } catch (Exception e) {
			            in = new BufferedInputStream(System.in, BS);
			        }
			    }
			 
			    private char getChar() {
			        while (bId == size) {
			            try {
			                size = in.read(buf);
			            } catch (Exception e) {
			                return NC;
			            }
			            if (size == -1) return NC;
			            bId = 0;
			        }
			        return (char) buf[bId++];
			    }
			 
			    public int nextInt() {
			        return (int) nextLong();
			    }
			 
			    public int[] nextInts(int N) {
			        int[] res = new int[N];
			        for (int i = 0; i < N; i++) {
			            res[i] = (int) nextLong();
			        }
			        return res;
			    }
			 
			    public long[] nextLongs(int N) {
			        long[] res = new long[N];
			        for (int i = 0; i < N; i++) {
			            res[i] = nextLong();
			        }
			        return res;
			    }
			 
			    public long nextLong() {
			        cnt = 1;
			        boolean neg = false;
			        if (c == NC) c = getChar();
			        for (; (c < '0' || c > '9'); c = getChar()) {
			            if (c == '-') neg = true;
			        }
			        long res = 0;
			        for (; c >= '0' && c <= '9'; c = getChar()) {
			            res = (res << 3) + (res << 1) + c - '0';
			            cnt *= 10;
			        }
			        return neg ? -res : res;
			    }
			 
			    public double nextDouble() {
			        double cur = nextLong();
			        return c != '.' ? cur : cur + nextLong() / cnt;
			    }
			 
			    public double[] nextDoubles(int N) {
			        double[] res = new double[N];
			        for (int i = 0; i < N; i++) {
			            res[i] = nextDouble();
			        }
			        return res;
			    }
			 
			    public String next() {
			        StringBuilder res = new StringBuilder();
			        while (c <= 32) c = getChar();
			        while (c > 32) {
			            res.append(c);
			            c = getChar();
			        }
			        return res.toString();
			    }
			 
			    public String nextLine() {
			        StringBuilder res = new StringBuilder();
			        while (c <= 32) c = getChar();
			        while (c != '\n') {
			            res.append(c);
			            c = getChar();
			        }
			        return res.toString();
			    }
			 
			    public boolean hasNext() {
			        if (c > 32) return true;
			        while (true) {
			            c = getChar();
			            if (c == NC) return false;
			            else if (c > 32) return true;
			        }
			    }
			}

					     static class Pair implements Comparable<Pair>{
					            public long x, y,z;
					            public Pair(long x1, long y1,long z1) {
					                x=x1;
					                y=y1;
					                z=z1;
					            }
					             public Pair(long x1, long y1) {
					                x=x1;
					                y=y1;
					    
					            }
					            
					            @Override
					            public int hashCode() {
					                return (int)(x + 31 * y);
					            }
					            public String toString() {
					                return x + " " + y+" "+z;
					            }
					            @Override
					            public boolean equals(Object o){
					                if (o == this) return true;
					                if (o.getClass() != getClass()) return false;
					                Pair t = (Pair)o;
					                return t.x == x && t.y == y&&t.z==z;
					            }
					    public int compareTo(Pair o)
					    {
					    	
					    
					    	return (int)((o.y-o.x)-(y-x));
					     
					        }
					     
					    }
					    
					    }

					     
