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.text.DecimalFormat;
import java.util.*;

/**
 * Created by Katushka on 11.03.2020.
 */
public class Main {

    private static final DecimalFormat DF_2 = new DecimalFormat("0.00");

    static int[] readArray(int size, InputReader in) {
        int[] a = new int[size];
        for (int i = 0; i < size; i++) {
            a[i] = in.nextInt();
        }
        return a;
    }

    static long[] readLongArray(int size, InputReader in) {
        long[] a = new long[size];
        for (int i = 0; i < size; i++) {
            a[i] = in.nextLong();
        }
        return a;
    }

    private static final long MOD = 1000000007;

    public static void main(String[] args) throws FileNotFoundException {
//        InputReader in = new InputReader(new FileInputStream("input.txt"));
//        PrintWriter out = new PrintWriter(new BufferedOutputStream(new FileOutputStream("gangs.out")));

        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

        int t = in.nextInt();
        for (int ii = 0; ii < t; ii++) {
            int n = in.nextInt();
            long w = in.nextLong();
            long[][] ws = new long[n][2];
            for (int i = 0; i < n; i++) {
                ws[i][0] = in.nextLong();
                ws[i][1] = i + 1;
            }
            Arrays.sort(ws, new Comparator<long[]>() {
                @Override
                public int compare(long[] o1, long[] o2) {
                    return Long.compare(o1[0], o2[0]);
                }
            });

            int ind = binSearchRight(ws, w);
            if (ind < 0) {
                out.println(-1);
                continue;
            }
            long cur = 0;
            List<Long> ans = new ArrayList<>();
            for (int i = ind; i >= 0; i--) {
                cur += ws[i][0];
                ans.add(ws[i][1]);
                if (cur >= (w + 1) / 2) {
                    break;
                }
            }
            if (cur >= (w + 1) / 2) {
                out.println(ans.size());
                outputArray(ans, out);
            } else {
                out.println(-1);
            }
        }

        out.close();
    }

    static int binSearchRight(long[][] list, long key) {
        int l = -1;
        int r = list.length;
        while (l < r - 1) {
            int m = (l + r) / 2;
            if (list[m][0] <= key) {
                l = m;
            } else {
                r = m;
            }
        }
        return l;
    }

    private static double scc(Collection<Integer>[] edges, Collection<Integer>[] invEdges) {
        List<Integer> p = new ArrayList<>();
        int n = edges.length;
        boolean[] visited = new boolean[n];

        for (int i = 0; i < n; i++) {
            if (!visited[i]) {
                dfs1(i, edges, p, visited);
            }
        }

        int[] comps = new int[n];
        Arrays.fill(comps, -1);
        int comp = 0;
        Set<Integer>[] compEdges = new HashSet[n];
        Set<Integer>[] invCompEdges = new HashSet[n];

        for (int i = n - 1; i >= 0; i--) {
            if (comps[p.get(i)] == -1) {
                compEdges[comp] = new HashSet<>();
                invCompEdges[comp] = new HashSet<>();
                dfs2(p.get(i), invEdges, comps, comp);
                comp++;
            }
        }

        int m = comp;

        int[] compSizes = new int[m];

        for (int i = 0; i < n; i++) {
            compSizes[comps[i]]++;
            for (int to : edges[i]) {
                if (comps[i] != comps[to]) {
                    compEdges[comps[i]].add(comps[to]);
                    invCompEdges[comps[to]].add(comps[i]);
                }
            }
        }
        Set<Integer> starts = new HashSet<>();
        for (int i = 0; i < m; i++) {
            if (invCompEdges[i].isEmpty()) {
                starts.add(i);
            }
        }

        return bfs(starts, compEdges, m, compSizes, invCompEdges);
    }

    private static double bfs(Set<Integer> start, Set<Integer>[] graph, int n, int[] compSizes, Set<Integer>[] invCompEdges) {
        Queue<Integer> q = new LinkedList<>();
        Set<Integer>[] parents = new Set[n];
        for (int i = 0; i < n; i++) {
            parents[i] = new HashSet<>();
        }
        boolean[] visited = new boolean[n];
        for (Integer v : start) {
            q.add(v);
            visited[v] = true;
            parents[v].add(v);
        }
        double res = start.size();

        while (!q.isEmpty()) {
            int v = q.poll();
            outer:
            for (int to : graph[v]) {
                if (!visited[to]) {
                    for (int p : invCompEdges[to]) {
                        if (parents[p].isEmpty()) {
                            continue outer;
                        }
                    }
                }
                if (!visited[to]) {
                    visited[to] = true;
                    q.add(to);
                    parents[to] = new HashSet<>();
                    parents[to].add(to);
                    for (int p : invCompEdges[to]) {
                        parents[to].addAll(parents[p]);
                    }
                    double sum = 0;
                    for (Integer p : parents[to]) {
                        sum += compSizes[p];
                    }
                    res += compSizes[to] * 1.0 / sum;
                }
            }
        }

        return res;
    }

    private static int dfs2(int v, Collection<Integer>[] invEdges, int[] comps, int comp) {
        if (comps[v] != -1) {
            return 0;
        }
        comps[v] = comp;
        int cnt = 1;
        for (Integer to : invEdges[v]) {
            cnt += dfs2(to, invEdges, comps, comp);
        }
        return cnt;
    }

    private static int dfs1(int v, Collection<Integer>[] edges, List<Integer> p, boolean[] visited) {
        visited[v] = true;
        int cnt = 1;
        for (Integer to : edges[v]) {
            if (!visited[to]) {
                cnt += dfs1(to, edges, p, visited);
            }
        }
        p.add(v);
        return cnt;
    }


    private static void outputArray(List<Long> ans, PrintWriter out) {
        StringBuilder str = new StringBuilder();
        for (long an : ans) {
            str.append(an).append(' ');
        }
        out.println(str);
    }

    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                createTokenizer();
            }
            return tokenizer.nextToken();
        }

        private void createTokenizer() {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public String nextWord() {
            return next();
        }

        public String nextString() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

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

        public double nextDouble() {
            return Double.parseDouble(next());
        }

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

        public char nextChar() {
            return next().charAt(0);
        }

        public int[] nextInts() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                createTokenizer();
            }
            List<Integer> res = new ArrayList<>();
            while (tokenizer.hasMoreElements()) {
                res.add(Integer.parseInt(tokenizer.nextToken()));
            }
            int[] resArray = new int[res.size()];
            for (int i = 0; i < res.size(); i++) {
                resArray[i] = res.get(i);
            }
            return resArray;
        }
    }
}