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

public class Codeforces {

    public static void main(String[] args) throws IOException {
        FastScanner fs = new FastScanner();
        PrintWriter pw = new PrintWriter(System.out);
        int t = 0;
        t = fs.getInt();
        while (t-- > 0) {
            int n = fs.getInt(); // 2*10^5
            long w = fs.getLong(); // 10^18
            long[] ar = fs.getLongArray(n); // 10^9

            long l = Utility.ceil(w, 2);
            long r = w;

            boolean hasAnswer = false;
            long sum = 0;
            List<Integer> indices = new ArrayList<>();

            for (int i = 0; i < ar.length; i++) {
                if (ar[i] < l) {
                    sum += ar[i];
                    indices.add(i);
                    if (sum >= l) {
                        hasAnswer = true;
                        break;
                    }
                } else if (ar[i] >= l && ar[i] <= r) {
                    indices.clear();
                    indices.add(i);
                    hasAnswer = true;
                    break;
                }
            }

            if (!hasAnswer) {
                pw.println(-1);
                continue;
            }
            pw.println(indices.size());
            for (Integer i : indices) {
                pw.print((i + 1) + " ");
            }
            pw.println();

        }
        pw.close();
    }

}

class MOD {
    static long mod = 1000000007;

    static long add(long x, long y) {
        long result = x + y;
        return result > mod ? result - mod : result;
    }

    static long sub(long x, long y) {
        long result = x - y;
        return result < 0 ? result + mod : result;
    }

    static long mul(long x, long y) {
        long result = x * y;
        return result >= mod ? result % mod : result;
    }

    static long pow(long x, long y) {
        long result = 1;
        x %= mod;
        while (y > 0) {
            if ((y & 1) == 1)
                result = mul(result, x);
            x = mul(x, x);
            y = y >>> 1;
        }
        return result;
    }

    static long modInv(long x) {
        return pow(x, mod - 2);
    }

}

class Utility {

    static int ceil(int a, int b) {
        if (a == 0)
            return 0;
        return (a - 1) / b + 1;
    }

    static long ceil(long a, long b) {
        if (a == 0)
            return 0;
        return (a - 1) / b + 1;
    }

    static int gcd(int a, int b) {
        if (a > b) {
            int t = a;
            a = b;
            b = t;
        }
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    static long gcd(long a, long b) {
        if (a > b) {
            long t = a;
            a = b;
            b = t;
        }
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    static int binarySearch(int[] ar, int x, int start, int end) {
        int l = start;
        int r = end;
        while (l <= r) {
            int mid = l + (r - l) / 2;
            if (ar[mid] == x) {
                return mid;
            } else if (ar[mid] > x) {
                r = mid - 1;
            } else {
                l = mid + 1;
            }
        }
        return -1;
    }

    static int lowerBound(int[] ar, int x) {
        int l = 0;
        int r = ar.length - 1;
        while (l <= r) {
            int mid = l + (r - l) / 2;

            if (ar[mid] >= x)
                r = mid - 1;
            else
                l = mid + 1;
        }
        return r + 1;
    }

    static int upperBound(int[] ar, int x) {
        int l = 0;
        int r = ar.length - 1;
        while (l <= r) {
            int mid = l + (r - l) / 2;

            if (ar[mid] > x)
                r = mid - 1;
            else
                l = mid + 1;
        }
        return l;
    }

    static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a)
            l.add(i);
        Collections.sort(l);
        for (int i = 0; i < a.length; i++)
            a[i] = l.get(i);
    }

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

    static boolean isPalindrome(String s) {
        char[] ss = s.toCharArray();
        int i = 0;
        int j = s.length() - 1;

        while (i < j) {
            if (ss[i] != ss[j]) {
                return false;
            }
            i += 1;
            j -= 1;
        }
        return true;
    }

    static boolean isPrime(int n) {
        if (n <= 1)
            return false;
        else if (n == 2)
            return true;
        else if (n % 2 == 0)
            return false;
        for (int i = 3; i * i <= n; i += 2) {
            if (n % i == 0)
                return false;
        }
        return true;
    }

    static void printArray(int[] ar) {
        for (int i = 0; i < ar.length; i++) {
            System.out.print(ar[i] + " ");
        }
        System.out.println();
    }

    static void printArray(long[] ar) {
        for (int i = 0; i < ar.length; i++) {
            System.out.print(ar[i] + " ");
        }
        System.out.println();
    }

    static void printIntList(List<Integer> list) {
        for (int i = 0; i < list.size(); i++) {
            System.out.print(list.get(i) + " ");
        }
        System.out.println();
    }

    static void printLongList(List<Long> list) {
        for (int i = 0; i < list.size(); i++) {
            System.out.print(list.get(i) + " ");
        }
        System.out.println();
    }

    static long choose(long n, long k) {
        if (n < k)
            return 0;
        if (k == 0 || k == n)
            return 1;
        return choose(n - 1, k - 1) + choose(n - 1, k);
    }

    static List<Integer> divisors(int n) {
        List<Integer> list = new ArrayList<>();
        for (int i = 1; i * i < n; i++) {
            if (n % i == 0)
                list.add(i);
        }
        for (int i = (int) Math.sqrt(n); i >= 1; i--) {
            if (n % i == 0)
                list.add(n / i);
        }
        return list;
    }

}

class Pair implements Comparable<Pair> {
    Integer first;
    Integer second;

    Pair(Integer f, Integer s) {
        this.first = f;
        this.second = s;
    }

    public String toString() {
        return "(" + this.first + ", " + this.second + ")";
    }

    @Override
    public boolean equals(Object object) {
        if (((Pair) object).first == this.first && ((Pair) object).second == this.second && object instanceof Pair) {
            return true;
        } else {
            return false;
        }
    }

    @Override
    public int hashCode() {
        return (String.valueOf(first) + ":" + String.valueOf(second)).hashCode();
    }

    @Override
    public int compareTo(Pair p) {
        int f = first.compareTo(p.first);
        if (f != 0)
            return f;

        return Integer.compare(second, p.second);
    }
}

class FastScanner {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = new StringTokenizer("");

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

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

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

    int[] getIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = getInt();
        return a;
    }

    long[] getLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = getLong();
        return a;
    }

    List<Integer> getIntList(int n) {
        List<Integer> list = new ArrayList<>();
        for (int i = 0; i < n; i++)
            list.add(getInt());
        return list;
    }

    List<Long> getLongList(int n) {
        List<Long> list = new ArrayList<>();
        for (int i = 0; i < n; i++)
            list.add(getLong());
        return list;
    }
}