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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
public class Main{
   static class Item{
       int index,Weight;
       public Item(int index,int Weight){
           this.index=index;
           this.Weight=Weight;
       }
   }
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
//        Scanner sc= new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int t=sc.nextInt();
        outer:while (t-->=1) {
            int n = sc.nextInt();
            long w = sc.nextLong();
            ArrayList<Item> items = new ArrayList<Item>();
            long totalWeight = 0;
            Item totake = null;
            for (int i = 0; i < n; i++) {
                int wi = sc.nextInt();
                if (wi > w) {
                    continue;
                }
                if (wi >= (w + 1) / 2) {
                    totake = new Item(i + 1, wi);
                } else {
                    if (totalWeight + wi <= w) {
                        items.add(new Item(i+1,wi));
                        totalWeight += wi;
                    }
                }
            }
            if (totake != null) {
                System.out.println(1);
                System.out.println(totake.index);
            } else if (totalWeight >= (w + 1) / 2) {
                System.out.println(items.size());
                for (Item i : items) {
                    System.out.print(i.index+" ");

                }
            } else {
                System.out.println(-1);
            }
        }





        out.flush();

    }
    //-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

    static void sort(int[] a) {
        ArrayList<Integer> l=new ArrayList<>();
        for (int i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }
    static String sortString(String s){
        char temp[]=s.toCharArray();
        Arrays.sort(temp);
        return new String(temp);
    }

    static class Pair implements Comparable<Pair> {
        int num, val;

        public Pair(int a, int b) {
            num = a;
            val = b;
        }

        public int compareTo(Pair x) {
            return x.val-val;
        }
    }
    static int mod=(int)1e9+7;
    static long mod(long x){
        return ((x%mod+mod)%mod);
    }
    static long add(long x,long y){
        return mod(mod(x)+mod(y));
    }
    static long mul(long x,long y){
        return mod(mod(x)*mod(y));
    }
    static int[] find(int n,int start,int diff){
        int a[]= new int[n];
        a[0]=start;
        for (int i=1;i<n;i++)a[i]=a[i-1]+diff;
        return a;
    }
    static void swap(int a,int b){
        int c=a;
        a=b;
        b=c;
    }

    static void printArray(int a[]){
        for (int i=0;i<a.length;i++){
            System.out.print(a[i]+" ");
        }
    }
    static boolean sorted(int a[]){
        int n=a.length;
        boolean flag=true;
        for (int i=0;i<n-1;i++){
            if (a[i]>a[i+1])flag=false;
        }
        if (flag)return true;
        else  return false;
    }
    public static int findlog(long n){
        if(n == 0)
            return 0;

        if(n == 1)
            return 0;
        if(n == 2)
            return 1;
        double num = Math.log(n);
        double den = Math.log(2);
        if(den == 0)
            return 0;
        return (int)(num/den);
    }
    public static long gcd(long a,long b){
        if(b%a == 0)
            return a;
        return gcd(b%a,a);
    }
    public static int gcdInt(int a,int b){

        if(b%a == 0)
            return a;

        return gcdInt(b%a,a);

    }

    static void sortReverse(long[] a) {
        ArrayList<Long> l=new ArrayList<>();
        for (long i:a) l.add(i);
//        Collections.sort.(l);
        Collections.sort(l,Collections.reverseOrder());
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }

    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long[] readArrayLong(long n) {
            long[] a=new long[(int)n];
            for (int i=0; i<n; i++) a[i]=nextLong();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }


}