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.util.*;
import java.lang.*;
import java.io.*;

public class Codeforces {
    static FastReader sc=new FastReader();
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		PrintWriter out=new PrintWriter(System.out);
		StringBuffer sb=new StringBuffer();
		int t=I();
		while(t-->0)
		{
			int n=I();
			long w=L();
			pair a[]=new pair[n];
			for(int i=0;i<n;i++){
				a[i]=new pair(L(),i);
			}
			Arrays.sort(a,new myComp());
			int j=n-1;
			for(;j>=0;j--){
				if(a[j].a<=w){
					break;
				}
			}
			StringBuffer sb1=new StringBuffer();
			int ans=0;
			long wans=0;
			for(;j>=0;j--){
				if(wans+a[j].a<(w+2-1)/2){
					sb1.append((a[j].b+1)+" ");
					wans+=a[j].a;
					ans++;
				}else if((wans+a[j].a)>=(w+2-1)/2 && (wans+a[j].a)<=w){
					sb1.append((a[j].b+1)+" ");
					wans+=a[j].a;
					ans++;
					break;
				}
			}
			if(wans<(w+2-1)/2){
				sb.append("-1\n");
			}else{
				sb.append(ans+"\n");
				sb.append(sb1+"\n");
			}
		}
		out.print(sb.toString());
		out.close();
	}
	public static boolean palindrome(String s,int n)
	{
		for(int i=0;i<=n/2;i++){
			if(s.charAt(i)!=s.charAt(n-i-1)){
				return false;
			}
		}
		return true;
	}
	public static void DFS(ArrayList<Integer> arr[],int s,boolean visited[])
	{
		visited[s]=true;
		for(int i:arr[s]){
			if(!visited[i]){
				DFS(arr,i,visited);
			}
		}
	}
	public static int BS(long a[],long x,int ii,int jj)
	{
		// int n=a.length;
		int mid=0;
		int i=ii,j=jj;
		while(i<=j)
		{
			mid=(i+j)/2;
			if(a[mid]>x)
			j=mid-1;
			else if(a[mid]<=x)
			i=mid+1;
		}
		if(a[mid]>x && mid>ii)
		return mid-1;
		else
		return mid;
	}
	public static ArrayList<Integer> prime(int n)
	{
	    ArrayList<Integer> arr=new ArrayList<>();
	    boolean prime[] = new boolean[n + 1];
        for (int i = 0; i <= n; i++)
        prime[i] = true;
        for (int p = 2; p * p <= n; p++)
        {
            if (prime[p] == true)
            {
                for (int i = p * p; i <= n; i += p)
                prime[i] = false;
            }
        }
        for (int i = 2; i <= n; i++)
        {
            if (prime[i] == true)
            arr.add(i);
        }
        return arr;
	}

	// Fenwick / BinaryIndexed  Tree  USE IT - FenwickTree ft1=new FenwickTree(n);
	public static class FenwickTree
	{
		long farr[];
		int n;
		public FenwickTree(int c)
		{
			n=c+1;
			farr=new long[n];
		}
		public void update_range(int l,int r,long p)
		{
			update(l,p);
			update(r+1,(-1)*p);
		}
		public void update(int x,long p)
		{
			for(;x<n;x+=x&(-x))
			{
				farr[x]+=p;
			}
		}
		public long get(int x)
		{
			long ans=0;
			for(;x>0;x-=x&(-x))
			{
				ans=ans+farr[x];
			}
			return ans;
		}
	}

	//Disjoint Set Union
	public static class DSU
	{
	    static int par[],rank[];
	    public DSU(int c)
	    {
	        par=new int[c+1];
	        rank=new int[c+1];
	        for(int i=0;i<=c;i++)
	        {
	            par[i]=i;
	            rank[i]=0;
	        }
	    }
	    public static int find(int a)
	    {
	        if(a==par[a])
	        return a;
	        return par[a]=find(par[a]);
	    }
	    public static void union(int a,int b)
	    {
	        int a_rep=find(a),b_rep=find(b);
	        if(a_rep==b_rep)
	        return;
	        if(rank[a_rep]<rank[b_rep])
	        par[a_rep]=b_rep;
	        else if(rank[a_rep]>rank[b_rep])
	        par[b_rep]=a_rep;
	        else
	        {
	            par[b_rep]=a_rep;
	            rank[a_rep]++;
	        }
	    }
	}

	//SEGMENT TREE CODE

	// public static void segmentUpdate(int si,int ss,int se,int qs,int qe,long x)
	// {
	// 	if(ss>qe || se<qs)return;
	// 	if(qs<=ss && qe>=se)
	// 	{
	// 		seg[si][0]+=1L;
	// 		seg[si][1]+=x*x;
	// 		seg[si][2]+=2*x;
	// 		return;
	// 	}
	// 	int mid=(ss+se)/2;
	// 	segmentUpdate(2*si+1,ss,mid,qs,qe,x);
	// 	segmentUpdate(2*si+2,mid+1,se,qs,qe,x);
	// }
	// public static long segmentGet(int si,int ss,int se,int x,long f,long s,long t,long a[])
	// {
	// 	if(ss==se && ss==x)
	// 	{
	// 		f+=seg[si][0];
	// 		s+=seg[si][1];
	// 		t+=seg[si][2];
	// 		long ans=a[x]+(f*((long)x+1L)*((long)x+1L))+s+(t*((long)x+1L));
	// 		return ans;
	// 	}
	// 	int mid=(ss+se)/2;
	// 	if(x>mid){
	// 		return segmentGet(2*si+2,mid+1,se,x,f+seg[si][0],s+seg[si][1],t+seg[si][2],a);
	// 	}else{
	// 		return segmentGet(2*si+1,ss,mid,x,f+seg[si][0],s+seg[si][1],t+seg[si][2],a);
	// 	}
	// }

	public static class pair
    {
    	long a;
    	int b;
    	public pair(long val,int index)
    	{
    	    a=val;
    	    b=index;
    	}
    }
	public static class myComp implements Comparator<pair>
	{
		//sort in ascending order.
		public int compare(pair p1,pair p2)
		{
			if(p1.a==p2.a)
    	    return 0;
    	    else if(p1.a<p2.a)
    	    return -1;
    	    else
    	    return 1;
		}
		//sort in descending order.
		// public int compare(pair p1,pair p2)
    	// {
    	//     if(p1.a==p2.a)
    	//     return 0;
    	//     else if(p1.a<p2.a)
    	//     return 1;
    	//     else
    	//     return -1;
    	// }
	}
    public static class myComp1 implements Comparator<pair1>
    {
		//sort in ascending order.
    	public int compare(pair1 p1,pair1 p2)
    	{
    	    if(p1.a==p2.a)
    	    return 0;
    	    else if(p1.a<p2.a)
    	    return -1;
    	    else
    	    return 1;
    	}
		//sort in descending order.
		// public int compare(pair p1,pair p2)
    	// {
    	//     if(p1.a==p2.a)
    	//     return 0;
    	//     else if(p1.a<p2.a)
    	//     return 1;
    	//     else
    	//     return -1;
    	// }
    }
	public static class pair1
    {
    	long a;
    	long b;
    	public pair1(long val,long index)
    	{
    	    a=val;
    	    b=index;
    	}
    }
    public static ArrayList<pair1> mergeIntervals(ArrayList<pair1> arr)
	{
	    //****************use this in main function-Collections.sort(arr,new myComp1());
	    ArrayList<pair1> a1=new ArrayList<>();
	    if(arr.size()<=1)
	    return arr;
	    a1.add(arr.get(0));
	    int i=1,j=0;
	    while(i<arr.size())
	    {
	        if(a1.get(j).b<arr.get(i).a)
	        {
	           a1.add(arr.get(i));
	           i++;
	           j++;
	        }
	        else if(a1.get(j).b>arr.get(i).a && a1.get(j).b>=arr.get(i).b)
	        {
	            i++;
	        }
	        else if(a1.get(j).b>=arr.get(i).a)
	        {
	            long a=a1.get(j).a;
	            long b=arr.get(i).b;
	            a1.remove(j);
	            a1.add(new pair1(a,b));
	            i++;
	        }
	    }
	    return a1;
	}
	public static long countDigit(long n)
	{
	    long sum=0;
	    while(n!=0)
	    {
	        sum++;
	        n=n/10;
	    }
	    return sum;
	}
	public static long digitSum(long n)
	{
	    long sum=0;
	    while(n!=0)
	    {
	        sum=sum+n%10;
	        n=n/10;
	    }
	    return sum;
	}
	public static long gcd(long a,long b)
	{
	    if(b==0)
	    return a;
	    else
	    return gcd(b,a%b);
	}
	public static void sort(int[] A)
	{
        int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i)
		{
            int tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
        Arrays.sort(A);
    }
    public static void sort(long[] A)
	{
	    int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i)
		{
            long tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
	    Arrays.sort(A);
	}
    public static int I(){return sc.I();}
    public static long L(){return sc.L();}
    public static String S(){return sc.S();}
    public static double D(){return sc.D();}
}
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 I(){ 
        return Integer.parseInt(next());
    }
    long L(){ 
        return Long.parseLong(next());
    }
    double D(){
         return Double.parseDouble(next());
    }
    String S(){
        String str = "";
        try 
        {
            str = br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
        return str;
    }
}