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.*;
import java.util.stream.Collectors;

public class C {

    public static void main(String[] args) throws Exception {

        FastScanner sc = new FastScanner();
        FastWriter writer = new FastWriter();

        int t = sc.nextInt();
        while(t-- > 0) {
            int n = sc.nextInt();
            long W = sc.nextLong();
            int ar[] = sc.nextIntArray(n);
            long k = (W + 1) / 2;
            boolean found = false;
            for(int i = 0; i < n; i++) {
                if(ar[i] >= k && ar[i] <= W) {
                    writer.println(1);
                    writer.println(i + 1);
                    found = true;
                    break;
                }
            }
            if(found)
                continue;
            Pair nums[] = new Pair[n];
            for(int i=0;i<n;i++)
                nums[i] = new Pair(ar[i], i+1);
            sort(nums);

            Set<Integer> ans = new HashSet<>();
            long s = 0;

            for(int i = n-1; i >= 0; i--) {
                if(nums[i].x > W)
                    continue;
                if(s + nums[i].x > W)
                    continue;
                s += nums[i].x;
                ans.add(nums[i].y);
                if(s >= k && s <= W)
                    break;
            }
            if(s < k || s > W)
                writer.println(-1);
            else {
                writer.println(ans.size());
                for(int i : ans)
                    writer.print(i + " ");
                writer.println("");
            }
        }
        writer.close();
    }

    static final Random random = new Random();

    static class FastScanner {
        private InputStream sin = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        public FastScanner(){}
        public FastScanner(String filename) throws FileNotFoundException {
            File file = new File(filename);
            sin = new FileInputStream(file);
        }
        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            }else{
                ptr = 0;
                try {
                    buflen = sin.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while(true){
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                }else if(b == -1 || !isPrintableChar(b) || b == ':'){
                    return minus ? -n : n;
                }else{
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }
        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
            return (int) nl;
        }
        public double nextDouble() { return Double.parseDouble(next());}
        public long[] nextLongArray(final int n){
            final long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
        public int[] nextIntArray(final int n){
            final int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }
        public double[] nextDoubleArray(final int n){
            final double[] a = new double[n];
            for (int i = 0; i < n; i++)
                a[i] = nextDouble();
            return a;
        }

        public List<Integer>[] adjacencyList(int nodes, int edges) {
            return adjacencyList(nodes, edges, false);
        }
        public List<Integer>[] adjacencyList(int nodes, int edges, boolean isDirected) {

            List<Integer>[] adj = new ArrayList[nodes + 1];
            Arrays.setAll(adj, (i) -> new ArrayList<>());
            for (int i = 0; i < edges; i++) {
                int a = nextInt(), b = nextInt();
                adj[a].add(b);
                if (!isDirected) adj[b].add(a);
            }
            return adj;
        }
    }

    static class FastWriter {

        BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));
        void print(int n) throws Exception { writer.write(n + ""); }
        void println(int n) throws Exception { writer.write(n + "\n"); }

        void print(long n) throws Exception { writer.write(n + ""); }
        void println(long n) throws Exception { writer.write(n + "\n"); }

        void print(String s) throws Exception { writer.write(s); }
        void println(String s) throws Exception { writer.write(s); writer.newLine(); }

        void println(int ar[]) throws Exception { for(int e : ar) writer.write(e + " "); writer.newLine(); }
        void println(long ar[]) throws Exception { for(long e : ar) writer.write(e + " "); writer.newLine(); }
        void println(double ar[]) throws Exception { for(double e : ar) writer.write(e + " "); writer.newLine(); }
        void close() throws Exception { writer.close(); }
        <T> void println(List<T> L) throws Exception { for(T o : L) writer.write(o + " "); writer.newLine(); }
    }

    static int findDistance(List<Integer> G[], int nodes, int src, int dst) {

        LinkedList<Integer> queue = new LinkedList<>();
        int dist[] = new int[nodes + 1];
        int ans = -1;
        dist[src] = 0;
        queue.add(src);
        while(queue.size() > 0) {
            int u = queue.poll();
            if(u == dst) {
                ans = dist[u];
            }
            for(int v : G[u]) {
                if(dist[v] >= 0)
                    continue;
                queue.add(v);
                dist[v] = dist[u] + 1;
            }
        }
        return ans;
    }

    static void sort(List<Integer> A) {
        shuffleList(A);
        Collections.sort(A);
    }

    static void shuffleList(List<Integer> A) {
        int n = A.size();
        for(int i = 0; i < n; i++) {
            int tmp = A.get(i);
            int randomPos = i + random.nextInt(n-i);
            A.set(i, A.get(randomPos));
            A.set(randomPos, tmp);
        }
    }

    static void sort(int A[]) {
        shuffleArray(A);
        Arrays.sort(A);
    }
    static void sort(long A[]) {
        shuffleArray(A);
        Arrays.sort(A);
    }
    static void sort(double A[]) {
        shuffleArray(A);
        Arrays.sort(A);
    }
    static <T> void sort(T[] A) {
        shuffleArray(A);
        Arrays.sort(A);
    }
    static <T> void shuffleArray(T[] A) {
        int n = A.length;
        for(int i = 0; i < n; i++) {
            T tmp = A[i];
            int randomPos = i + random.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
    }
    static void shuffleArray(int[] A) {
        int n = A.length;
        for(int i = 0; i < n; i++) {
            int tmp = A[i];
            int randomPos = i + random.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
    }
    static void shuffleArray(long[] A) {
        int n = A.length;
        for(int i = 0; i < n; i++) {
            long tmp = A[i];
            int randomPos = i + random.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
    }
    static void shuffleArray(double[] A) {
        int n = A.length;
        for(int i = 0; i < n; i++) {
            double tmp = A[i];
            int randomPos = i + random.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
    }

    static int[] subArray(int A[], int x, int y) {
        int B[] = new int[y - x + 1];
        for(int i = x; i <= y; i++)
            B[i-x] = A[i];
        return B;
    }

    static int[] toArray(List<Integer> L) {
        return L.stream().mapToInt(x -> x).toArray();
    }

    static void println(int[] A) {
        for(int e: A) System.out.print(e + " ");
        System.out.println();
    }

    static void println(long[] A) {
        for(long e: A) System.out.print(e + " ");
        System.out.println();
    }

    static void println(List arr) {
        for(Object e: arr) System.out.print(e + " ");
        System.out.println();
    }

    static <T> void println(T A[]) {

        for(T i : A)
            System.out.print(i + " ");
        System.out.println();
    }

    static void print(String s) {
        System.out.print(s);
    }
    static void println(long n) {
        System.out.println(n);
    }

    static void println(String s) {
        System.out.println(s);
    }

    static List<Integer> toList(int ar[]) {
        return Arrays.stream(ar).boxed().collect(Collectors.toList());
    }

    static List<Long> toList(long ar[]) {
        return Arrays.stream(ar).boxed().collect(Collectors.toList());
    }

    static List<Double> toList(double ar[]) {
        return Arrays.stream(ar).boxed().collect(Collectors.toList());
    }

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

    private static int abs(int a){  return (a>=0) ? a: -a;  }
    private static int min(int... ins){ return Arrays.stream(ins).min().getAsInt(); }
    private static int max(int... ins){ return Arrays.stream(ins).max().getAsInt(); }
    private static int sum(int... ins){ return Arrays.stream(ins).sum(); }
    private static long abs(long a){ return (a>=0) ? a: -a; }
    private static long min(long... ins){ return Arrays.stream(ins).min().getAsLong(); }
    private static long max(long... ins){ return Arrays.stream(ins).max().getAsLong(); }
    private static long sum(long... ins){ return Arrays.stream(ins).sum(); }
    private static double abs(double a){ return (a>=0) ? a: -a; }
    private static double min(double... ins){ return Arrays.stream(ins).min().getAsDouble(); }
    private static double max(double... ins){ return Arrays.stream(ins).max().getAsDouble(); }
    private static double sum(double... ins){ return Arrays.stream(ins).sum(); }

    private static class Pair implements Comparable<Pair> {
        int x, y;
        Pair(int x, int y) { this.x = x; this.y = y; }
        Pair() {}

        @Override
        public int compareTo(Pair other) {
            return x == other.x ? y - other.y : x - other.x;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair pair = (Pair) o;
            return x == pair.x &&
                    y == pair.y;
        }

        @Override
        public int hashCode() {
            return Objects.hash(x, y);
        }
    }

    static int pow(long n, int p, int mod) {
        if(p == 0)
            return 1;
        long x = pow(n, p/2, mod);
        x = x * x % mod;
        return (int) ( p % 2 == 0 ? x : x * n % mod );
    }

    static long inv(int x, int m) {
        return pow(x, m - 2, m);
    }

    static int lowerBound(int ar[], int L, int R, int val) {
        if(val < ar[L] || val > ar[R])
            return -1;
        while(L <= R) {
            int mid = (L + R) / 2;
            if(ar[mid] >= val)
                R = mid - 1;
            else
                L = mid + 1;
        }
        return ar[L] == val ? L : -1;
    }

    static int upperBound(int ar[], int L, int R, int val) {
        if(val < ar[L] || val > ar[R])
            return -1;
        while(L <= R) {
            int mid = (L + R) / 2;
            if(ar[mid] > val)
                R = mid - 1;
            else
                L = mid + 1;
        }
        return ar[R] == val ? R : -1;
    }
}