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:
//package cf683;

import java.io.*;
import java.util.*;
import java.util.function.Function;
import java.util.stream.Collectors;

// What's the smallest input?
// Check * for int/long overflow.
// Check / for accidental rounding.
// Are you using doubles? Can you avoid it?
// Never compare after taking mod.
// Mod the final result.
// Initialize globals in solve() unless they are independent of the problem input.
// Check for local/global name conflicts (n?).
// Check initial values for max/min (not Integer.MIN_VALUE for long).
public class C {
    static Random rand;
    static boolean MULTIPLE_CASES = true;
    static boolean CONSTRUCTIVE = false;
    static long MOD = (long) 1e9 + 7;
    static long BIG = (long) 2e9 + 10;

    public static void solve(Reader in, PrintWriter out) {
        int n = in.ni();
        long W = in.nl();
        long lb = W/2 + (W % 2 == 1 ? 1 : 0);
        // sum everything < lb
        // if we encounter anything on [lb, W], just use it alone
        
        long[] items = in.nls(n);
        List<Integer> knapsack = new ArrayList<>();
        long sum = 0;
        for (int i = 0; i < n; i++) {
            if (items[i] < lb) {
                knapsack.add(i+1);
                sum += items[i];
            } else if (items[i] <= W) {
                knapsack = new ArrayList<>();
                knapsack.add(i+1);
                sum += items[i];
                break;
            }

            if (sum >= lb) {
                break;
            }
        }

        if (sum < lb) {
            out.println(-1);
        } else {
            out.println(knapsack.size());
            for (long i : knapsack) {
                out.print(i + " ");
            }
            out.println();
        }
    }

    public static void main(String[] args) throws IOException {
        Reader in = null;
        PrintWriter out = null;
        for (String arg : args) {
            if (arg.startsWith("input")) {
                in = new Reader(arg);
            } else if (arg.startsWith("output")) {
                out = new PrintWriter(new FileWriter(arg));
            }
        }
        if (in == null) in = new Reader();
        if (out == null) out = new PrintWriter(new OutputStreamWriter(System.out));

        if (MULTIPLE_CASES) {
            int tests = in.ni();
            for (int t = 0; t < tests; t++) {
                solve(in, out);
            }
        } else {
            solve(in, out);
        }

        out.flush();
    }

    static class Tester {
        public static void main(String[] args) throws IOException {
            Validator validator = new Validator();

            File currentDir = new File(".");
            long before;
            long after;
            for (File inputFile : Arrays.stream(currentDir.listFiles())
                    .sorted(Comparator.comparing(File::getName))
                    .collect(Collectors.toList())) {
                if (!inputFile.getName().startsWith("input")
                        || inputFile.getName().contains("sight")
                        || inputFile.getName().contains("big")) continue;
                System.out.println("Test file: " + inputFile.getName());

                before = System.nanoTime();
                String outputFileName = "output" + inputFile.getName().substring(5);
                C.main(new String[]{inputFile.getName(), outputFileName});
                after = System.nanoTime();

                File outputFile = new File(outputFileName);
                if (!outputFile.exists()) {
                    throw new IllegalStateException("Missing output file " + outputFile);
                }

                // TODO if verifier is implemented, remove this
                if (CONSTRUCTIVE) {
                    System.out.println("INPUT:");
                    printFile(inputFile);
                    System.out.printf("\nOUTPUT: (%d milliseconds)\n", (after - before) / 1000000L);
                    printFile(outputFile);
                    continue;
                }

                if (validator.validate(inputFile, outputFile)) {
                    System.out.printf("OK (%d milliseconds)\n", (after - before) / 1000000L);
                } else {
                    System.out.println("FAILED");
                    System.out.println("\nInput: ");
                    printFile(inputFile);
                    System.out.println("\nIncorrect Output: ");
                    printFile(outputFile);
                    return;
                }
            }
            System.out.println("\n-----------------\n");

            File sightTestInput = new File("input-sight");
            if (sightTestInput.exists()) {
                System.out.println("Running sight test... Input:");
                printFile(sightTestInput);
                before = System.nanoTime();
                System.out.println("\nOutput: ");
                C.main(new String[]{"input-sight"});
                after = System.nanoTime();
                System.out.printf("(%d milliseconds)\n", (after - before) / 1000000L);
                System.out.println("\n-----------------\n");
            }

            File bigTestInput = new File("input-big");
            if (bigTestInput.exists()) {
                System.out.println("Running big test...");
                before = System.nanoTime();
                C.main(new String[]{"input-big"});
                after = System.nanoTime();
                System.out.printf("(%d milliseconds)\n", (after - before) / 1000000L);
            }
        }

        static void printFile(File file) throws FileNotFoundException {
            BufferedReader reader = new BufferedReader(new FileReader(file));
            reader.lines().forEach(System.out::println);
        }
    }

    static class Validator {
        boolean validate(File inputFile, File outputFile) throws IOException {
            File expectedOutputFile = new File("expected-output" + inputFile.getName().substring(5));
            if (CONSTRUCTIVE || !expectedOutputFile.exists()) {
                return validateManual(inputFile, outputFile);
            }
            return areSame(outputFile, expectedOutputFile);
        }

        private boolean validateManual(File inputFile, File outputFile) throws IOException {
            if (CONSTRUCTIVE) {
                // Validate output against input
                Reader inputReader = new Reader(inputFile.getName());
                Reader outputReader = new Reader(outputFile.getName());

                // TODO implement manual validation

                throw new IllegalStateException("Missing expected output file");
            } else {
                File naiveOutput = new File("naive-" + outputFile.getName());
                Naive.main(new String[]{inputFile.getName(), naiveOutput.getName()});

                return areSame(outputFile, naiveOutput);
            }
        }

        private boolean areSame(File file1, File file2) throws IOException {
            BufferedReader reader1 = new BufferedReader(new FileReader(file1));
            BufferedReader reader2 = new BufferedReader(new FileReader(file2));

            String line1;
            while ((line1 = reader1.readLine()) != null) {
                String line2 = reader2.readLine();
                if (line2 == null) line2 = ""; // ok if one has an extra newline
                if (!line1.trim().equals(line2.trim())) {
                    return false;
                }
            }
            String line2;
            while ((line2 = reader2.readLine()) != null) {
                if (!line2.trim().isEmpty()) {
                    return false;
                }
            }
            return true;
        }

    }

    static class Naive {
        public static void solveNaive(Reader in, PrintWriter out) {
            throw new IllegalStateException("missing expected output file");
        }

        public static void main(String[] args) throws IOException {
            Reader in = null;
            PrintWriter out = null;
            for (String arg : args) {
                if (arg.startsWith("input")) {
                    in = new Reader(arg);
                } else if (arg.startsWith("naive-output")) {
                    out = new PrintWriter(new FileWriter(arg));
                }
            }
            if (in == null) in = new Reader();
            if (out == null) out = new PrintWriter(new OutputStreamWriter(System.out));

            int tests = in.ni();
            for (int t = 0; t < tests; t++) {
                solveNaive(in, out);
            }

            out.flush();
            out.close();
        }
    }

    static boolean isPowerOfTwo(int x) {
        return x > 0 & (x & (x - 1)) == 0;
    }

    static int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    static void ruffleSort(int[] a) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int oi = rand.nextInt(n), temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }

    static void ruffleSort(long[] a) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int oi = rand.nextInt(n);
            long temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }

    ///////////////////////////////////
    //////////   FAST PAIR   //////////
    ///////////////////////////////////

    // Works on -1e9 <= x, y <= 1e9
    static long pair(int x, int y) {
        x = (int) BIG / 2 - x;
        y = (int) BIG / 2 - y;
        return x * BIG + y;
    }

    static int x(long pair) {
        return (int) BIG / 2 - (int) (pair / BIG);
    }

    static int y(long pair) {
        return (int) BIG / 2 - (int) (pair % BIG);
    }

    static String str(long pair) {
        return String.format("(%d, %d)", x(pair), y(pair));
    }

    ///////////////////////////////////
    ////////// BINARY SEARCH //////////
    ///////////////////////////////////

    // return highest in range that still returns true
    // T T T F F F F
    // invariant:
    // -    indicator(min) = true
    // -    indicator(max+1) = false
    static int binarySearchHighest(int min, int max, Function<Integer, Boolean> indicator) {
        int a = min;
        int b = max;
        while (a != b) {
            int mid = (a % 2 != b % 2) ? 1 + (a + b) / 2 : (a + b) / 2;
            if (indicator.apply(mid)) {
                a = mid;
            } else {
                b = mid - 1;
            }
        }
        return a;
    }

    // return lowest in range that still returns true
    // F F F F T T T
    // invariant:
    // -    indicator(min-1) = false
    // -    indicator(max) = true
    static int binarySearchLowest(int min, int max, Function<Integer, Boolean> indicator) {
        int a = min;
        int b = max;
        while (a != b) {
            int mid = (a + b) / 2;
            if (indicator.apply(mid)) {
                b = mid;
            } else {
                a = mid + 1;
            }
        }
        return a;
    }

    static void insist(boolean bool) {
        if (!bool) throw new IllegalStateException();
    }

    static class Reader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public Reader() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        public Reader(String fileName) throws FileNotFoundException {
            reader = new BufferedReader(new FileReader(fileName));
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

        public int[] nis(int n) {
            int[] out = new int[n];
            for (int i = 0; i < n; i++) {
                out[i] = ni();
            }
            return out;
        }

        public long[] nls(int n) {
            long[] out = new long[n];
            for (int i = 0; i < n; i++) {
                out[i] = nl();
            }
            return out;
        }
    }
}