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:

import java.lang.reflect.Array;
import java.util.*;
import java.util.function.Function;
import java.util.stream.Collectors;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;
import java.io.*;
import java.math.*;

public class CC
{
    static class pair implements Comparable<pair>
    {
        int x;
        long y;
        pair(int x,long y){
            this.x=x;
            this.y=y;
        }


        public int compareTo(pair o)
        {
            return (int)(y-o.y);
        }

    }

    public static void main(String[] args)
    {
        StringBuffer sb = new StringBuffer();
        int t=i();
   while (t-->0)
        {

            long n=l(),W=l();
            long A[]=new long[(int)n];
            int gr=0;
            for(int i=0;i<n;i++)
            {
                A[i] = l();
                if(A[i]>W)
                    gr++;

            }
        long cw=W/2+W%2;

            if(gr==n)
               sb.append("-1"+"\n");//false
            else
                {

                    ArrayList<Integer>l=new ArrayList<>();

                    int flag=0;

                    for(int i=0;i<n;i++)
                    {
                        if(A[i]>=cw&&A[i]<=W)
                        {
                            flag=1;
                            sb.append("1"+"\n"+(i+1)+"\n");
                            break;
                        }
                    }



                    if(flag==0)
                    {
                        ArrayList<Integer>ind=new ArrayList<>();
                        for(int i=0;i<n;i++)
                        {
                            if(A[i]<(cw))
                                ind.add(i);
                        }

                        long sum=0;
                        int j=0;
                int ffff=0;
                        for(int i=0;i<ind.size();i++)
                        {
                            sum+=A[ind.get(i)];
                           l.add(ind.get(i));
                            if(sum>=cw&&sum<=W)
                            {
                                sb.append(l.size()+"\n");
                                for(int u:l)
                                    sb.append((u+1)+" ");
                                sb.append("\n");
                                ffff=1;
                                break;
                            }
                        }
                        if(ffff==0)
                            sb.append(-1+"\n");




                    }




            }





        }
        System.out.println(sb.toString());
    }


 //********************************Class pair******************************************************************************************************************************************///////////////////////////////////////////////////////////////////////////////////////////////

//-------------------prime factorization********/***************************************************************************************************************************************///////////////////////////////////
static TreeMap primefactorize(long n)
{
    TreeMap<Integer,Integer>h=new TreeMap<>();
    long number=n;
    for(int i=2;i<=Math.sqrt(n);i++)
    {
        if(n%i==0)
        {
            int cnt=0;
            while(n%i==0)
            {
                n=n/i;
                cnt++;
            }
            h.put(i,cnt);
        }
    }
    if(n!=1)
        h.put((int)n,1);
    return h;
}
///******************************SYSTEM PART*****************************************************************************************************************************************************************************************************************************************************////
    static InputReader in=new InputReader(System.in);
    static OutputWriter out=new OutputWriter(System.out);

    public static long pow(long a, long b)
    {
        long result=1;
        while(b>0){
            if (b % 2 != 0){
                result=(result*a);
                b--;
            }
            a=(a*a);
            b /= 2;
        }
        return result;
    }
    public static long gcd(long a, long b){
        if (a == 0){
            return b;
        }
        return gcd(b%a, a);
    }
    public static long lcm(long a, long b){
        return a*(b/gcd(a,b));
    }
    public static long l(){
        String s=in.String();
        return Long.parseLong(s);
    }
    public static void pln(String value){
        System.out.println(value);
    }
    public static int i(){
        return in.Int();
    }
    public static String s(){
        return in.String();
    }
}
///******************input Reader//***************************************************************************************************************************************************************************************
class InputReader
{
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
    public InputReader(InputStream stream) {
        this.stream = stream;
    }
    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 Int() {
        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 - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
    public String String() {
        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) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
    public String next() {
        return String();
    }
    public interface SpaceCharFilter
    {
        public boolean isSpaceChar(int ch);
    }
}

//*******************OUTPUT WRITER********************************************************************************************************************************************************************************************************************************************************//
class OutputWriter {
    private final PrintWriter writer;
    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }
    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }
    public void print(Object...objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }
    public void printLine(Object...objects) {
        print(objects);
        writer.println();
    }
    public void close() {
        writer.close();
    }
    public void flush() {
        writer.flush();
    }
}