Problem: You have a knapsack with the capacity of W. There are also n items, the i-th one has weight w_i. 

You want to put some of these items into the knapsack in such a way that their total weight C is at least half of its size, but (obviously) does not exceed it. Formally, C should satisfy: ⌈ W/2⌉ ≤ C ≤ W. 

Output the list of items you will put into the knapsack or determine that fulfilling the conditions is impossible. 

If there are several possible lists of items satisfying the conditions, you can output any. Note that you don't have to maximize the sum of weights of items in the knapsack.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4). Description of the test cases follows.

The first line of each test case contains integers n and W (1 ≤ n ≤ 200 000, 1≤ W ≤ 10^{18}). 

The second line of each test case contains n integers w_1, w_2, ..., w_n (1 ≤ w_i ≤ 10^9) — weights of the items.

The sum of n over all test cases does not exceed 200 000.

Output

For each test case, if there is no solution, print a single integer -1. 

If there exists a solution consisting of m items, print m in the first line of the output and m integers j_1, j_2, ..., j_m (1 ≤ j_i ≤ n, all j_i are distinct) in the second line of the output — indices of the items you would like to pack into the knapsack.

If there are several possible lists of items satisfying the conditions, you can output any. Note that you don't have to maximize the sum of weights items in the knapsack.

Example

Input


3
1 3
3
6 2
19 8 19 69 9 4
7 12
1 1 1 17 1 1 1


Output


1
1
-1
6
1 2 3 5 6 7

Note

In the first test case, you can take the item of weight 3 and fill the knapsack just right.

In the second test case, all the items are larger than the knapsack's capacity. Therefore, the answer is -1.

In the third test case, you fill the knapsack exactly in half.

Solution (in JAVA):

Solution:
//  package cp;
import java.util.*;
import java.io.*;
import java.math.*;
public class Cp_3 {
	BigInteger bi1=new BigInteger("2");//initialize as string
//	1.BigInteger bi=new BigInteger(Readers.next());- take input as biginteger
	StringBuilder sb=new StringBuilder();
//	2.StringBuilder temp=new StringBuilder(str[i-1]);
//	3.String rev=temp.reverse().toString(); convert sb to string
//	4.if(str[i].compareTo(rev)>=0)minn=0;-compare two Strings
//  5.(Initialize as string) - (a.add(b)) - (array initialized with null and not 0)
	Integer[] ARRE=new Integer[5];//Integer sort-TLE-Initialize object elements i.e a[0].
	static final int mod1 = 1000000007;//or 1e9+7
//	6.System.exit(0); to exit from code....esp in recur 
	long gcd(long a,long b) {if(b==0)return a;else return gcd(b,a%b);}
	static long ceil(double d) {return (long)Math.ceil(1.0*d);}
	int ch_int(char c) {return Integer.parseInt(String.valueOf(c));}//change char to Integer
	String ch_str(char c) {return String.valueOf(c);}
	String int_str(int num) {return Integer.toString(num);}
	void divisor(long n,int start) {
		int cnt=0;for(int i=start;i<=Math.sqrt(n);i++) {
		if(n%i==0) {if(i==n/i)cnt++;else cnt+=2;}}}
	  class Thing implements Comparable<Thing>{
	      public long val;
	      public int id;
	      
	      public Thing(int a, int i){
	         val = a;
	         id = i;
	      }
	      public int compareTo(Thing oth){
	         int lol = (int)(val-oth.val);
	         return lol;
	      }
	   }
	public static void main(String[] args) throws IOException {
		PrintWriter out = new PrintWriter(System.out);
		Readers.init(System.in);
		Cp_3 obj=new Cp_3();
		int t=Readers.nextInt();
//		Map<Long, Integer> map = new HashMap<>();
		for (int i = 0; i < t; i++) {
			int n=Readers.nextInt();
			long w=Readers.nextLong();
			int[] a=new int[n];
			ArrayList<Thing> ls = new ArrayList<Thing>();
			for (int j = 0; j < n; j++) {
				a[j]=Readers.nextInt();
//				map.put(a[j],(i+1));
			}
			int flag=0;
			for (int j = 0; j < n; j++) {
				if(a[j]>=Math.ceil(w*0.5) && a[j]<=w) {
					System.out.println(1);
					System.out.println((j+1));
					flag=1;
					break;
				}
			}
			if(flag==0) {
				ArrayList<Integer> ind=new ArrayList<>();
				long summ=0;
				for (int j = 0; j < n; j++) {
					if(a[j]>w)continue;
					else {
						summ+=a[j];
						ind.add(j+1);
						if(summ>=Math.ceil(w*0.5))break;
					}
				}
				if(ind.size()==0 || summ<Math.ceil(w*0.5))System.out.println(-1);
				else {
					System.out.println(ind.size());
					for (int j = 0; j <ind.size(); j++) {
						System.out.print(ind.get(j)+" ");
					}
				}
			}
		}
		out.flush();
	}
 
}
class Readers {
	 
    static BufferedReader reader;
    static StringTokenizer tokenizer;
 
    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }
    
    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary 
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
 
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
    
    static long nextLong() throws IOException{
		return Long.parseLong(next());
	}
 
}