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 com.company;


import javax.print.attribute.standard.PrinterIsAcceptingJobs;
import javax.sound.midi.spi.SoundbankReader;
import java.io.*;
import java.math.BigInteger;
import java.net.Inet4Address;
import java.text.CollationElementIterator;
import java.util.*;
import java.util.concurrent.CopyOnWriteArrayList;

public class Main implements Runnable {
    int size[];
    static int e9 = 1000000007;
    int max = Integer.MIN_VALUE;
    long max1 = Long.MIN_VALUE;
    long min1 = Long.MAX_VALUE;
    long fib[][];
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    int parent[];
    int rank[];
    ArrayList<ArrayList<Integer>> arrayLists;
    long fib1[][];
    long r[];
    int n;
    int m;
    long co=0;
    long size1[];
    long v[];
    int arr[][];
    int u=0;
    HashMap<Long,Long> hashMap=new HashMap<>();
    ArrayList<Pair> arrayList;
    public static void main(String[] args) throws IOException {
        new Thread(null,new Main(),"Main",1<<28).start();
    }

    public void run() {
        FastReader scanner = new FastReader();
//            Scanner scanner = new Scanner(System.in);
//            BufferedReader bufferedReader=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter printWriter = new PrintWriter(System.out);
        long t = scanner.nextLong();
        high:while (t-- > 0) {
            int n=scanner.nextInt();
            double w=scanner.nextLong();
            ArrayList<Pair> arrayList=new ArrayList<>();
            for (int i = 0; i < n; i++) {
                long a=scanner.nextLong();
                arrayList.add(new Pair(a,i));
            }
            Collections.sort(arrayList,new Sorting());
            long ans=0;
            long w1=(long)Math.ceil(w/2.0);
//            System.out.println(w1);
            int s=0;
            int e=0;
            int arr1[]=new int[n];
            long h=0;
            while (s<n&&e<n){
//                System.out.println(ans+arrayList.get(e).x);
                if(ans+arrayList.get(e).x<w1){
                    arr1[(int)arrayList.get(e).y]=-1;
                    ans+=arrayList.get(e).x;
                    e++;
                    h++;
                }
                else{
                    if(ans+arrayList.get(e).x>w){
//                        System.out.println("k");
                        arr1[(int)arrayList.get(s).y]=0;
                        ans-=arrayList.get(s).x;
                        s++;
                        h--;
                    }
                    else{
                        h++;
                        arr1[(int)arrayList.get(e).y]=-1;
                        ans+=arrayList.get(e).x;
                        break ;
                    }
                }
//                System.out.println(ans);
            }
//            System.out.println(ans);
            if(!(ans>=w1&&ans<=w)){
                printWriter.println(-1);
            }
            else {
                printWriter.println(h);
                for (int i = 0; i < n; i++) {
                    if (arr1[i] == -1) {
                        printWriter.print((i + 1) + " ");
                    }
                }
                printWriter.println();
            }
        }
        printWriter.flush();
    }
    static long mod=1_000_000_007;
    public long lcm(long a,long b){
        return (a*b)/gcd(a,b);
    }
    public long mul(long a, long b) {
//        System.out.println(a+" "+b);
        return ((a)*(b));
    }
    public long fact(int x) {
        long ans=1;
        for (int i=2; i<=x; i++) ans=mul(ans, i);
        return ans;
    }
    public long fastPow(long base, long exp) {
        if (exp==0) return 1;
        long half=fastPow(base, exp/2);
        if (exp%2==0) return mul(half, half);
        return mul(half, mul(half, base));
    }
    public long modInv(long x) {
        return fastPow(x, mod-2);
    }
    public long nCk(int n, int k) {
        return mul(fact(n), mul(modInv(fact(k)), modInv(fact(n-k))));
    }
    public void parent(int n){
        parent=new int[n+1];
        size=new int[n+1];
        rank=new int[n+1];
        for (int i = 0; i <=n; i++) {
            parent[i]=i;
            rank[i]=0;
//            size[i]=1;
        }
    }
    public void union(int i,int j){
        int root1=find(i);
        int root2=find(j);
//            if(root1 != root2) {
//                parent[root2] = root1;
////                sz[a] += sz[b];
//            }
        if(root1==root2){
            return;
        }
        if(rank[root1]>rank[root2]){
            parent[root2]=root1;
            size[root1]+=size[root2];
        }
        else if(rank[root1]<rank[root2]){
            parent[root1]=root2;
            size[root2]+=size[root1];
        }
        else{
            parent[root2]=root1;
            rank[root1]+=1;
            size[root1]+=size[root2];
        }
    }
    public int find(int p){
        if(parent[p]!=p){
            if(parent[p]==-1){
                return parent[p];
            }
            parent[p]=find(parent[p]);
        }
        return parent[p];
    }
    public double dist(double x1,double y1,double x2,double y2){
        double e=(x2-x1)*(x2-x1)+(y2-y1)*(y2-y1);
        double e1=Math.sqrt(e);
        return e1;
    }
    public void make(int p){
        parent[p]=p;
        rank[p]=1;
    }
    Random rand = new Random();
    public void sort(int[] a, int n) {
        for (int i = 0; i < n; i++) {
            int j = rand.nextInt(i + 1);
            int tmp = a[i];
            a[i] = a[j];
            a[j] = tmp;
        }
        Arrays.sort(a, 0, n);
    }
    public long gcd(long a,long b){
        if(b==0){
            return a;
        }
        return gcd(b,a%b);
    }
    //    public void dfs(ArrayList<Integer> arrayList){
//        for (int i = 0; i < arrayList.size(); i++) {
//            if(v1[arrayList.get(i)]==false){
//                v1[arrayList.get(i)]=true;
//                dfs(arrayLists.get(i));
//            }
//        }
//    }
    public double fact(double h){
        double sum=1;
        while(h>=1){
            sum=(sum%e9)*(h%e9);
            h--;
        }
        return sum%e9;
    }
    public long primef(double r){
        long c=0;
        long ans=1;
        long g=0;
        while(r%2==0){
            c++;
            r=r/2;
        }
        if(c>0){
            ans*=2;
        }
        c=0;
//            System.out.println(ans+" "+r);
        for (int i = 3; i <=Math.sqrt(r) ;i+=2) {
            g=0;
            while(r%i==0){
//                    System.out.println(i);
                c++;
                g++;
                r=r/i;
            }
            if(c>0){
                ans*=i;
            }
            c=0;
        }
        if(r>2){
            ans*=r;
        }
        return ans;
    }
    public long divisor(double r){
        long c=0;
//        if(n==3)
//            System.out.println(r+" "+n+" "+k+" "+"l");
        for (int i =2; i <=Math.sqrt(r); i++) {
            if(r%i==0){
                if(r/i==i){
                    c++;
                }
                else{
                    if(r/i<n){
                        c+=2;
                    }else{
                        c++;
                    }
                }
            }
        }
        return c;
    }
}
class Pair {
    long x;
    long y;
    int z;
    public Pair(long x,long y) {
        this.x = x;
        this.y = y;
//        this.z=z;
    }

    // @Override
//    public int hashCode() {
//        int hash = 37;
//        return this.x * hash + this.y;
//    }

//    @Override
//    public boolean equals(Object o1) {
//        if (o1 == null || o1.getClass() != this.getClass()) {
//            return false;
//        }
//        Pair o = (Pair) o1;
//        if (o.x == this.x && o.y == this.y) {
//            return true;
//        }
//        return false;
//    }
}
class Sorting implements Comparator<Pair> {
    public int compare(Pair p1, Pair p2) {
        if(p1.x==p2.x){
            return Long.compare(p1.y,p2.y);
        }else {
            return Long.compare(p1.x, p2.x);
        }
    }
}
class Edge{
    int s=0;
    int d=0;
    int c=0;
    public Edge(int s,int d,int c){
        this.s=s;
        this.d=d;
        this.c=c;
    }
}