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:
/**
 * @author vivek
 * programming is thinking, not typing
 */

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class C {

    static class Obj implements Comparable<Obj> {
        int ind;
        long val;

        Obj(int ind, long val) {
            this.ind = ind;
            this.val = val;
        }


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

    private static void solveTC(int __) {

        /* For Google */
//		ans.append("Case #").append(__).append(": ");

        //code start

        int n = scn.nextInt();
        long w = scn.nextLong();

        Obj[] arr = new Obj[n];
        for (int i = 0; i < n; i++) {
            arr[i] = new Obj(i + 1, scn.nextLong());
        }

        Arrays.sort(arr);

        int lim = -1;
        for (int i = 0; i < n; i++) {
            if (arr[i].val <= w) {
                lim = i;
            }
        }

        ArrayList<Integer> ans = new ArrayList<>();

        long lo = (w % 2 == 0) ? w / 2 : (w / 2) + 1;

        long sum = 0;
        for (int i = lim; i >= 0; i--) {
            sum += arr[i].val;
            if (sum > w) {
                sum -= arr[i].val;
                break;
            }
            ans.add(arr[i].ind);
        }

        if (sum < lo) {
            print("-1\n");
            return;
        }

        print(ans.size() + "\n");
        for (int e : ans) {
            print(e + " ");
        }

        //code end

        print("\n");
    }

    public static void main(String[] args) {
        scn = new Scanner();
        ans = new StringBuilder();
        int t = scn.nextInt();
//		int t = 1;

//        int limit=               ;
//        sieve(limit);

        /*
        try {
            System.setOut(new PrintStream(new File("file_i_o\\output.txt")));
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
*/
        for (int i = 1; i <= t; i++) {
            solveTC(i);
        }
        System.out.print(ans);
    }
    //Stuff for prime start

    /**
     * sorting algos
     */
    private static void sort(int[] arr) {
        ArrayList<Integer> li = new ArrayList<>(arr.length);
        for (int ele : arr) li.add(ele);
        Collections.sort(li);
        for (int i = 0; i < li.size(); i++) {
            arr[i] = li.get(i);
        }
    }

    private static void sort(long[] arr) {
        ArrayList<Long> li = new ArrayList<>(arr.length);
        for (long ele : arr) li.add(ele);
        Collections.sort(li);
        for (int i = 0; i < li.size(); i++) {
            arr[i] = li.get(i);
        }
    }

    private static void sort(float[] arr) {
        ArrayList<Float> li = new ArrayList<>(arr.length);
        for (float ele : arr) li.add(ele);
        Collections.sort(li);
        for (int i = 0; i < li.size(); i++) {
            arr[i] = li.get(i);
        }
    }

    private static void sort(double[] arr) {
        ArrayList<Double> li = new ArrayList<>(arr.length);
        for (double ele : arr) li.add(ele);
        Collections.sort(li);
        for (int i = 0; i < li.size(); i++) {
            arr[i] = li.get(i);
        }
    }

    /**
     * List containing prime numbers <br>
     * <b>i<sup>th</sup></b> position contains <b>i<sup>th</sup></b> prime number <br>
     * 0th index is <b>null</b>
     */
    private static ArrayList<Integer> listOfPrimes;

    /**
     * query <b>i<sup>th</sup></b> element to get if its prime of not
     */
    private static boolean[] isPrime;

    /**
     * Performs Sieve of Erathosnesis and initialise isPrime array and listOfPrimes list
     *
     * @param limit the number till which sieve is to be performed
     */
    private static void sieve(int limit) {
        listOfPrimes = new ArrayList<>();
        listOfPrimes.add(null);
        boolean[] array = new boolean[limit + 1];

        Arrays.fill(array, true);
        array[0] = false;
        array[1] = false;

        for (int i = 2; i <= limit; i++) {
            if (array[i]) {
                for (int j = i * i; j <= limit; j += i) {
                    array[j] = false;
                }
            }
        }
        isPrime = array;
        for (int i = 0; i <= limit; i++) {
            if (array[i]) {
                listOfPrimes.add(i);
            }
        }
    }
    //stuff for prime end

    /**
     * Calculates the Least Common Multiple of two numbers
     *
     * @param a First number
     * @param b Second Number
     * @return Least Common Multiple of <b>a</b> and <b>b</b>
     */
    private static long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }

    /**
     * Calculates the Greatest Common Divisor of two numbers
     *
     * @param a First number
     * @param b Second Number
     * @return Greatest Common Divisor of <b>a</b> and <b>b</b>
     */
    private static long gcd(long a, long b) {
        return (b == 0) ? a : gcd(b, a % b);
    }

    static void print(Object obj) {
        ans.append(obj.toString());
    }


    static Scanner scn;
    static StringBuilder ans;

    //Fast Scanner
    static class Scanner {
        BufferedReader br;
        StringTokenizer st;

        public Scanner() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
/*
            try {
                br = new BufferedReader(new
                        InputStreamReader(new FileInputStream(new File("file_i_o\\input.txt"))));
            } 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 n) {
            int[] array = new int[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextInt();
            }
            return array;
        }

        Integer[] nextIntegerArray(int n) {
            Integer[] array = new Integer[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextInt();
            }
            return array;
        }

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

        String[] nextStringArray() {
            return nextLine().split(" ");
        }

        String[] nextStringArray(int n) {
            String[] array = new String[n];
            for (int i = 0; i < n; i++) {
                array[i] = next();
            }
            return array;
        }
    }
}