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.math.*;
import java.io.*; 
 public class codeforces{
 
static FastReader scan=new FastReader();
 public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
  static LinkedList<Pair>edges[][];
  static LinkedList<Integer>Same[];
  static LinkedList<Integer>Dif[];
  static LinkedList<Integer>integers[];
static int []dx={1,-1,0,0};
static int []dy={0,0,1,-1};
int dx_8[]={1,1,1,0,0,-1,-1,-1};
int dy_8[]={-1,0,1,-1,1,-1,0,1};
 
static boolean prime[];
static long LCM(long a,long b){
    return (Math.abs(a*b))/gcd(a,b);
   }
   static long gcd(long a, long b) {
    if(a!=0&&b!=0)
        while((a%=b)!=0&&(b%=a)!=0);
    return a^b;
}
static int countSetBits(int n) 
    { 
        int count = 0; 
        while (n > 0) { 
            count += n & 1; 
            n >>= 1; 
        } 
        return count; 
    } 
 static void sieve(long n) 
    { 
        
        prime = new boolean[(int)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; 
            } 
        } 
    }  
    
    static int count;
 
  static boolean canTransmit[][]=new boolean[1000+5][1000+5];
 
    
    
    static boolean vis[][];
    static boolean light[][];
    static char grid[][]; 
            
           static boolean isprime(long x)
           {
            for(long i=2;i*i<=x;i++)
                if(x%i==0)
                    return false;
                return true;
           }
           static int ans=0,perm=0,FOR=0;
           static int n,m;
           static boolean valid(int x,int y)
           {
            return (x>=0&&x<n&&y>=0&&y<n&&grid[x][y]!='.');
           }
    static ArrayList<Pair>BRAINFUCK;
    static int area[]=new int[1000000];
    static int region[][]=new int[1001][1001];
    static int permiter[]=new int[1000000];
 
static int R;
    static void dfs(int x,int y)
    {
       // System.out.println(x+" "+y);
         if (x < 0 || x >= n || y < 0 || y >= n || !light[x][y] || vis[x][y]) return;
     vis[x][y]=true;
     if(edges[x][y].size()>0)
     {
        for(Pair p:edges[x][y]){
      if(!light[p.x][p.y]){
        light[p.x][p.y]=true;
        ans++;
        
        for(int i=0;i<4;i++)
        {
               if (p.x + dx[i] >= n || p.x+ dx[i] < 0) continue;
                    if (p.y + dy[i] >= n || p.y + dy[i] < 0) continue;
                    if(vis[p.x+dx[i]][p.y+dy[i]])
            dfs(p.x,p.y);
        }}
    }
 
        
     }
      for(int i=0;i<4;i++)
        {
            dfs(x+dx[i],y+dy[i]);
        }
        
    } 
    static int ret=0;
    static void findp(){
        ret=0;
       for(int i=0;i<n;i++)
       {
        for(int j=0;j<n;j++)
        {
            
            int r=region[i][j];
            if(r==0)
                continue;
            try{
            if(region[i-1][j]==0){
                 //out.println(r);
                permiter[r]++;
            }
        }
        catch(IndexOutOfBoundsException e)
        {
            permiter[r]++;
        }
            if(region[i][j+1]==0)
                permiter[r]++;
            if(region[i+1][j]==0)
                permiter[r]++;
            try{
            if(region[i][j-1]==0)
                permiter[r]++;
        }
        catch(IndexOutOfBoundsException e)
        {
            permiter[r]++;
        }
        
 
 
    }
 
       }
 
    }
    static long arr[];
    static int sz[]=new int[(int)1e5+5];
   
static int upper_bound(long e)
{
    int l=0,r=arr.length;
    while(l<r)
    {
        int mid=(l+r)/2;
        if(arr[mid]>e)
            r=mid;
        else 
            l=mid+1;
    }
    return l;
}
 
public static void main(String[] args)  throws IOException 
{
//java.util.Scanner scan=new java.util.Scanner(new File("lightson.in"));
 //PrintWriter out = new PrintWriter (new FileWriter("lightson.out"));
  //  System.out.println(~-1);
    
 
        //System.out.println(0^1);
 
//SUCK IT UP AND DO IT ALRIGHT
    //System.out.println((-1*1)%mod);
    int t=scan.nextInt();
    while(t-->0){
    int n=scan.nextInt();
    long W=scan.nextLong();
    
    ArrayList<Pair>items=new ArrayList<Pair>();
    
   
    Pair it=null;
    long total=0;
    for(int i=0;i<n;i++){
  int weight=scan.nextInt();
  if(weight>W)
    continue;
if(weight>=(W+1)/2)
    it=new Pair(weight,i+1);
else 
{
if(total+weight<=W)
{
    items.add(new Pair(weight,i+1));
    total+=weight;
}
}}
if(it!=null)
{
    out.println(1);
    out.println(it.y);
    continue;
}
else if(total>=(W+1)/2) 
{
    out.println(items.size());
for(Pair p:items)
out.print(p.y+" ");
out.println();
 
}
else 
out.println(-1);
 
 
      
 
}
 
 out.close();
 
//SEE UP 
 
}
 
static long powMod(long base, long exp, long mod) {
       if (base == 0 || base == 1) return base;
       if (exp == 0) return 1;
       if (exp == 1) return base % mod;
       long R = powMod(base, exp/2, mod) % mod;
       R *= R;
       R %= mod;
       if ((exp & 1) == 1) {
           return base * R % mod;
       }
       else return R % mod;
   }
static double dis(double x1,double y1,double x2,double y2)
{
    return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}
static long mod(long x,long y)
    {
        if(x<0)
            x=x+(-x/y+1)*y;
        return x%y;
    }
 public static  long pow(long b, long e) {
            long r = 1;
            while (e > 0) {
                if (e % 2 == 1) r = r * b ;
                b = b * b;
                e >>= 1;
            }
            return r;
        }
private static void sort(long[] arr) {
        List<Long> list = new ArrayList<>();
        for (long object : arr) list.add(object);
        Collections.sort(list);
        for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
    }
 public static class FastReader {
        BufferedReader br;
        StringTokenizer root;
        
 
        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        boolean hasNext(){
            String line;
            while(root.hasMoreTokens())
                return true;
            return false;
        }
 
        String next() {
            while (root == null || !root.hasMoreTokens()) {
                try {
                    root = new StringTokenizer(br.readLine());
                } catch (Exception addd) {
                    addd.printStackTrace();
                }
            }
            return root.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(next());
        }
 
        double nextDouble() {
            return Double.parseDouble(next());
        }
 
        long nextLong() {
            return Long.parseLong(next());
        }
 
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (Exception addd) {
                addd.printStackTrace();
            }
            return str;
        }
         public int[] nextIntArray(int arraySize) {
            int array[] = new int[arraySize];
 
            for (int i = 0; i < arraySize; i++) {
                array[i] = nextInt();
            }
 
            return array;
        }
}
 static class Pair implements Comparable<Pair>{
        public int x, y;
        public Pair(int x1, int y1) {
            x=x1;
            y=y1;
        }
        @Override
        public int hashCode() {
            return (int)(x + 31 * y);
        }
        public String toString() {
            return x + " " + y;
        }
        @Override
        public boolean equals(Object o){
            if (o == this) return true;
            if (o.getClass() != getClass()) return false;
            Pair t = (Pair)o;
            return t.x == x && t.y == y;
        }
public int compareTo(Pair o)
{
    return (x-o.y)-(o.x-y);
 
    }
 
static class pair{
    int i;
    int j;
pair(int i,int j){
    this.i=i;
    this.j=j;
}}}
 static class tuple{
        int x,y,z;
        tuple(int a,int b,int c){
            x=a;
            y=b;
            z=c;
        }
    }
    static class Edge{
        int d,w;
        Edge(int d,int w)
        {
            this.d=d;
            this.w=w;
        }
    }
}