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:
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author wilso
 */
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
public class codeforces {
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter pw = new PrintWriter(System.out);

        int t = sc.ni();
        for (int rep = 0; rep < t; rep++) {
            long n = sc.nl();
            long W = sc.nl();
            long[] arr = sc.longArray((int)(n));
            int[] deter = solve(arr, W);
            if (deter.length == 0) pw.println(-1);
            else {
                pw.println(deter.length);
                StringBuilder sb = new StringBuilder();
                for (int val : deter) sb.append((val+1) + " " );
                pw.println(sb.toString());
            }
        }
        
        
        pw.close();
    }
    static int[] solve(long[] arr, long W) {
        List<Integer> list = new ArrayList();
        long lower_bound = W / 2;
        if (W % 2 == 1) lower_bound++;
        
        long rs = 0;
        boolean wedidit = false;
        for (int i = 0; i < arr.length; i++) {
            if (arr[i] > W) continue;
            if (arr[i] >= lower_bound && arr[i] <= W) {
                return new int[]{i};
            }
            if (arr[i] < lower_bound) {
                rs += arr[i];
                list.add(i);
                if (rs >= lower_bound && rs <= W) {
                    wedidit = true;
                    break;
                }
            }
            
        }
        if (wedidit) {
            int[] ret = new int[list.size()];
            for (int i = 0; i < ret.length; i++) ret[i] = list.get(i);
            return ret;
        }
        else {
            return new int[]{};
        }
   
       
        
    }
    
    
    static long pow(long num, long exp, long mod){
        long ans=1;
        for(int i=1;i<=exp;i++){
            ans=(ans*num)%mod;
        }
        return ans;
    }
    static boolean isPrime(int n)
    {
 
        // Check if number is less than
        // equal to 1
        if (n <= 1)
            return false;
 
        // Check if number is 2
        else if (n == 2)
            return true;
 
        // Check if n is a multiple of 2
        else if (n % 2 == 0)
            return false;
 
        // If not, then just check the odds
        for (int i = 3; i <= Math.sqrt(n); i += 2) 
        {
            if (n % i == 0)
                return false;
        }
        return true;
    }
    static int gcd(int a, int b)
    {
        if (a == 0)
            return b; 
        return gcd(b % a, a); 
    }
     
    // method to return LCM of two numbers
    static int lcm(int a, int b)
    {
        return (a / gcd(a, b)) * b;
    }
    public static void sort(int[] arr) {
        Random rgen = new Random();
        for (int i = 0; i < arr.length; i++) {
            int r = rgen.nextInt(arr.length);
            int temp = arr[i];
            arr[i] = arr[r];
            arr[r] = temp;
        }
        Arrays.sort(arr);
    }
 
    public static void sort(long[] arr) {
        Random rgen = new Random();
        for (int i = 0; i < arr.length; i++) {
            int r = rgen.nextInt(arr.length);
            long temp = arr[i];
            arr[i] = arr[r];
            arr[r] = temp;
        }
        Arrays.sort(arr);
    }
     
    public static void sort(int[][] arr) {
        //Sort an array (immune to quicksort TLE)
        Random rgen = new Random();
        for (int i = 0; i < arr.length; i++) {
            int randomPosition = rgen.nextInt(arr.length);
            int[] temp = arr[i];
            arr[i] = arr[randomPosition];
            arr[randomPosition] = temp;
        }
        Arrays.sort(arr, new Comparator<int[]>() {
            @Override
            public int compare(int[] a, int[] b) {
                if (a[1] > b[1])
                    return 1;
                else if (a[1] < b[1])
                    return -1;
                else
                    return 0;
            }
        });
    }
}

class FastScanner {
    BufferedReader br;
    StringTokenizer st;

    public FastScanner() {
        br = new BufferedReader(new InputStreamReader(System.in), 32768);
        st = null;
    }

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

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

    int[] intArray(int N) {
        int[] ret = new int[N];
        for (int i = 0; i < N; i++)
            ret[i] = ni();
        return ret;
    }

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

    long[] longArray(int N) {
        long[] ret = new long[N];
        for (int i = 0; i < N; i++)
            ret[i] = nl();
        return ret;
    }

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

    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}

class MultiSet {
    TreeMap<Integer, Integer> map = new TreeMap<>();
    public MultiSet() {
    }
    public void add(int val) {
        map.put(val, map.getOrDefault(val, 0) + 1);
    }
    public void remove(int val) {
        map.put(val, map.get(val) - 1);
        if (map.get(val) == 0) {
            map.remove(val);
        }
    }
    public Integer higher(int val) {
        return map.higherKey(val);
    }
    public Integer lower(int val) {
        return map.lowerKey(val);
    }
    public Integer ceiling(int val) {
        return map.ceilingKey(val);
    }
    public Integer floor(int val) {
        return map.floorKey(val);
    }
    public Integer first() {
        return map.firstKey();
    }
    public int last() {
        return map.lastKey();
    }
    public boolean isEmpty() {
        return map.isEmpty();
    }
}