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.io.BufferedReader;
import java.io.*;
import java.util.*;

public class a {

 static class Node implements Comparable<Node> {

   	long val;
   	int index;

   public Node(int i,long v){
   	this.val = v;
   	index = i;
   }
   @Override
   public int compareTo(Node o2){
   	return (int )(this.val-o2.val);
   }
   }
   
    static BufferedReader br;
    static long mod = 1000000000 + 7;
    static HashSet<Integer> p = new HashSet<>();
     static boolean debug =true;
           //  Arrays.sort(time  , (a1,a2) -> (a1[0]-a2[0])); 2d array sort lamda
    public static void main(String[] args) throws Exception {
        br = new BufferedReader(new InputStreamReader(System.in));
        int tc = 1;
        tc = cinI();
        PrintWriter pr =new PrintWriter(System.out);
        while (tc-- > 0) {

              long[] nw =readArray(2,0);
              int  n =(int)nw[0];
              long w = nw[1];

             Node[] ar=new Node[n];
           long[]  a=readArray(n,0);

             for(int i=0;i<n;i++){
             	//System.out.println(ar[i].length);
             	ar[i]=new Node(i+1,a[i]);
             }
             Arrays.sort(ar);
             boolean an =false;
             for(int i=0;i<n;i++){
             	if(ar[i].val>=(w+1)/2 && ar[i].val<=w){
                        an=true;
                        pr.println(1);
             		pr.println(ar[i].index);
             		break;
             	}
             }
             if(an)continue;
             // for(int i=0;i<n;i++){
             // 	pr.print(ar[0][i]+" ");
             // }
             // pr.println();
             // for(int i=0;i<n;i++){
             // 	pr.print(ar[1][i]+" ");
             // }
         long sum=0;
             long c = (w+1)/2;
                int l = 0;
                int ri=0;
             for(int r=0;r<n;r++){
                    sum+=ar[r].val;
                     if(sum>=c && sum<=w){
                     	ri=r;
                     	break;
                     }
                     while(sum>w){
                     	if(sum<=w && sum>=c){
                     		ri=r;
                     		break;
                     	}
                     	if(sum<c){

                     		break;
                     	}
                     	sum=sum-ar[l].val;
                     	l+=1;
                     }
             }
               long ans=0;
 
             for(int i=l;i<=ri;i++){
                 ans+=ar[i].val;               
             }
             if(ans<c || ans>w){
             	pr.println(-1);
             	continue;
             }
             pr.println(ri-l+1);
             for(int i=l;i<=ri;i++){
             	pr.print(ar[i].index+" ");
             }
             pr.println();
        }
        pr.close();
    }

    public static <E> void print(String var ,E e){
      if(debug==true){
      System.out.println(var +" "+e);
      }
    }
     private static long[]  sort(long[] e){
     ArrayList<Long> x=new ArrayList<>();
     for(long c:e){
       x.add(c);
     }
     Collections.sort(x);
     long[] y = new long[e.length];
     for(int i=0;i<x.size();i++){
       y[i]=x.get(i);
     }
     return y;
     }
    public static void printDp(long[][] dp) {

        int n = dp.length;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < dp[0].length; j++) {
                System.out.print(dp[i][j] + " ");
            }
            System.out.println();
        }
    }

    


  

    private static long gcd(long a, long b) {
        if (a == 0)
            return b;
        if (b == 0)
            return a;

        // base case
        if (a == b)
            return a;

        // a is greater
        if (a > b)
            return gcd(a % b, b);
        return gcd(a, b % a);
    }


    public static long min(long a, long b) {
        return Math.min(a, b);
    }

    public static int min(int a, int b) {
        return Math.min(a, b);
    }


    public static void sieve() {
        int[] pf = new int[100000000 + 1];
        //0 prime //1 not prime
        pf[0] = 1;
        pf[1] = 1;
        for (int j = 2; j <= 10000; j++) {

            if (pf[j] == 0) {
                p.add(j);
                for (int k = j * j; k < pf.length; k += j) {
                    pf[k] = 1;
                }
            }
        }

    }


    public static int[] readArray(int n, int x, int z) throws Exception {
        int[] arr = new int[n];
        String[] ar = cinA();
        for (int i = x; i < n + x; i++) {
            arr[i] = getI(ar[i - x]);
        }
        return arr;
    }

    public static long[] readArray(int n, int x) throws Exception {
        long[] arr = new long[n];
        String[] ar = cinA();
        for (int i = x; i < n + x; i++) {
            arr[i] = getL(ar[i - x]);
        }
        return arr;
    }

    public static void arrinit(String[] a, long[] b) throws Exception {
        for (int i = 0; i < a.length; i++) {
            b[i] = Long.parseLong(a[i]);
        }
    }

    public static HashSet<Integer>[] Graph(int n, int edge, int directed) throws Exception {
        HashSet<Integer>[] tree = new HashSet[n];

        for (int j = 0; j < edge; j++) {

            String[] uv = cinA();
            int u = getI(uv[0]);
            int v = getI(uv[1]);
            if (directed == 0) {

                tree[v].add(u);
            }
            tree[u].add(v);
        }
        return tree;
    }

    public static void arrinit(String[] a, int[] b) throws Exception {
        for (int i = 0; i < a.length; i++) {
            b[i] = Integer.parseInt(a[i]);
        }
    }


    static double findRoots(int a, int b, int c) {
        // If a is 0, then equation is not
        //quadratic, but linear


        int d = b * b - 4 * a * c;
        double sqrt_val = Math.sqrt(Math.abs(d));


        // System.out.println("Roots are real and different \n");

        return Math.max((double) (-b + sqrt_val) / (2 * a),
                (double) (-b - sqrt_val) / (2 * a));


    }

    public static String cin() throws Exception {
        return br.readLine();
    }

    public static String[] cinA() throws Exception {
        return br.readLine().split(" ");
    }

    public static String[] cinA(int x) throws Exception {
        return br.readLine().split("");
    }

    public static String ToString(Long x) {
        return Long.toBinaryString(x);
    }

    public static void cout(String s) {
        System.out.println(s);
    }

    public static Integer cinI() throws Exception {
        return Integer.parseInt(br.readLine());
    }

    public static int getI(String s) throws Exception {
        return Integer.parseInt(s);
    }

    public static long getL(String s) throws Exception {
        return Long.parseLong(s);
    }

    public static long max(long a, long b) {
        return Math.max(a, b);
    }

    public static int max(int a, int b) {
        return Math.max(a, b);
    }

    public static void coutI(int x) {
        System.out.println(String.valueOf(x));
    }

    public static void coutI(long x) {
        System.out.println(String.valueOf(x));
    }

    public static Long cinL() throws Exception {
        return Long.parseLong(br.readLine());
    }

    public static void arrInit(String[] arr, int[] arr1) throws Exception {
        for (int i = 0; i < arr.length; i++) {
            arr1[i] = getI(arr[i]);
        }

    }
}