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:
/*
								"जय श्री कृष्णा"
*/
import java.util.*;
import java.io.*;

public class C_Knapsack implements Runnable
{

    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            this.br = new BufferedReader(new InputStreamReader(System.in));
        }
        public FastReader(String s)
        {
            try
            {
                this.br = new BufferedReader(new FileReader(s));
            }
            catch (FileNotFoundException e)
            {
                e.printStackTrace();
            }
        }

        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[] nextIntArray(int size)
        {
            int[] arr = new int[size];
            for (int i = 0; i < size; ++i)
                arr[i] = nextInt();
            return arr;
        }

        long[] nextLongArray(int size)
        {
            long[] arr = new long[size];
            for (int i = 0; i < size; ++i)
                arr[i] = nextLong();
            return arr;
        }

        double[] nextDoubleArray(int size)
        {
            double[] arr = new double[size];
            for (int i = 0; i < size; ++i)
                arr[i] = nextDouble();
            return arr;
        }
    }
    static class FastWriter
    {
        PrintWriter pw;

        public FastWriter()
        {
            this.pw = (new PrintWriter(new BufferedOutputStream(System.out)));
        }

        public FastWriter(String s)
        {
            try
            {
                this.pw = new PrintWriter(new File(s));
            }
            catch (FileNotFoundException e)
            {
                e.printStackTrace();
            }
        }

        public void print(Object object)
        {
            pw.append("" + object);
        }

        public void println(Object object)
        {
            print(object);
            pw.append("\n");
        }

        public void println()
        {
            pw.append("\n");
        }

        public void close()
        {
            pw.close();
        }

        public void flush()
        {
            pw.flush();
        }

    }


    static int mod = (int) (1e9 + 7), N = (int) (1e5), INF = Integer.MAX_VALUE, NINF = Integer.MIN_VALUE;
    static final FastReader fr = new FastReader();
    static final FastWriter out = new FastWriter();
    public static void main(String[] args) throws java.lang.Exception
    {
        new Thread(null, new C_Knapsack(), "Main", 1 << 26).start();
    }

    long n, W, a[], limit, dp[][];

    static class Pair implements Comparable<Pair>
    {
        long x, y;

        Pair(long x, long y)
        {
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Pair o)
        {
            return Long.compare(this.x, o.x);
        }

    }
    void solve()
    {
        int n = fr.nextInt();
        W = fr.nextLong();
        a = fr.nextLongArray(n);

        limit = CP.ceil_div(W, 2);
        long val = 0;
        List<Long> al = new ArrayList<>();

        Pair p[] = new Pair[n];

        for(int i = 0; i < n; ++i)
            p[i] = new Pair(a[i], i + 1);
        Arrays.sort(p);


        for(int i = 0; i < n; ++i)
        {
            if(p[i].x > W)
                continue;
            if(p[i].x <= W && p[i].x >= limit)
            {
            	out.print("1\n"+p[i].y);
            	return;
            }

            if(val <= W && val >= limit)
                break;
            if(val + p[i].x <= W)
            {
                val += p[i].x;
                al.add(p[i].y);
            }
        }

        if(val < limit )
        {
            out.print(-1);
            return;
        }
        out.print(al.size() + "\n");
        for(Long x : al)
            out.print(x + " ");




    }
    @Override
    public void run()
    {
        long start = System.nanoTime(); // Program Start
        boolean testcase = true;
        int t = testcase ? fr.nextInt() : 1;
        while (t-- > 0)
        {
            solve();
            out.print("\n");
            out.flush();
        }
        out.close();
        long end = System.nanoTime(); // Program End
    }

    static class CP
    {

        static boolean isPrime(long n)
        {
            if (n <= 1)
                return false;
            if (n == 2 || n == 3)
                return true;
            if (n % 2 == 0 || n % 3 == 0)
                return false;
            for (int i = 5; i * i <= n; i += 6)
            {
                if (n % i == 0 || n % (i + 2) == 0)
                    return false;
            }
            return true;
        }
        static List<Integer> sieve(int size)
        {
            ArrayList<Integer> pr = new ArrayList<Integer>();
            boolean prime[] = new boolean[size];
            for(int i = 2; i < prime.length; i++)  prime[i] = true;
            for(int i = 2; i * i < prime.length; i++)
            {
                if(prime[i])
                {
                    for(int j = i * i; j < prime.length; j += i)
                    {
                        prime[j] = false;
                    }
                }
            }
            for(int i = 2; i < prime.length; i++) if(prime[i]) pr.add(i);
            return pr;
        }

        static long binary_Expo(long a, long b)   // calculating a^b
        {
            long res = 1;
            while (b != 0)
            {
                if ((b & 1) == 1)
                {
                    res *= a;
                    --b;
                }
                a *= a;
                b /= 2;
            }
            return res;
        }

        static long Modular_Expo(long a, long b)
        {
            long res = 1;
            while (b != 0)
            {
                if ((b & 1) == 1)
                {
                    res = (res * a) % mod;
                    --b;
                }
                a = (a * a) % mod;
                b /= 2;
            }
            return res;
        }

        static int i_gcd(int a, int b)  // iterative way to calculate gcd.
        {
            while (true)
            {
                if (b == 0)
                    return a;
                int c = a;
                a = b;
                b = c % b;
            }
        }

        static long gcd(long a, long b)  // here b is the remainder
        {
            if (b == 0)
                return a; //because each time b will divide a.
            return gcd(b, a % b);
        }

        static long ceil_div(long a, long b)   // a numerator b denominator
        {
            return (a + b - 1) / b;
        }

        static int getIthBitFromInt(int bits, int i)
        {
            return (bits >> (i - 1)) & 1;
        }

        static int upper_Bound(int a[], int x)  //closest to the left+1
        {
            int l = -1, r = a.length;
            while (l + 1 < r)
            {
                int m = (l + r) >>> 1;
                if (a[m] <= x)
                    l = m;
                else
                    r = m;
            }
            return l + 1;
        }

        static int lower_Bound(int a[], int x)  //closest to the right
        {
            int l = -1, r = a.length;
            while (l + 1 < r)
            {
                int m = (l + r) >>> 1;
                if (a[m] >= x)
                    r = m;
                else
                    l = m;
            }
            return r;
        }
        static boolean isSquarefactor(int x, int factor, int target)
        {
            int s = (int)Math.round(Math.sqrt(x));
            return factor * s * s == target;
        }

        static boolean isSquare(int x)
        {
            int s = (int)Math.round(Math.sqrt(x));
            return x * x == s;
        }
        static void sort(int a[])
        {
            PriorityQueue<Integer> q = new PriorityQueue<>();
            for (int i = 0; i < a.length; i++)
                q.add(a[i]);
            for (int i = 0; i < a.length; i++)
                a[i] = q.poll();
        }

        static int getMax(int arr[], int n)
        {
            int mx = arr[0];
            for (int i = 1; i < n; i++)
                if (arr[i] > mx)
                    mx = arr[i];
            return mx;
        }
        static int[] z_function(String s)
        {
            int n = s.length(), z[] = new int[n];

            for(int i = 1, l = 0, r = 0; i < n; ++i)
            {
                if(i <= r)
                    z[i] = Math.min(z[i - l], r - i + 1);

                while(i + z[i] < n && s.charAt(z[i]) == s.charAt(i + z[i]))
                    ++z[i];

                if(i + z[i] - 1 > r)
                {
                    l = i;
                    r = i + z[i] - 1;
                }
            }
            return z;
        }
    }

}