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.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.List;
import java.util.StringTokenizer;
import java.util.stream.Stream;

public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		Scanner in = new Main().new Scanner(inputStream);
		Writer out = new Main().new Writer(outputStream);
		Main solver = new Main();
		solver.solve(in, out);
	}

	public void solve(Scanner in, Writer out) {
		int t = in.ni();
		while (t-- > 0) {
			int n = in.ni();
			long W = in.nl();
			long[] k = in.nla(n);
			Integer[] indices = new Integer[n];
			for (int i = 0; i < n; i++) {
				indices[i] = i;
			}
			Arrays.sort(indices, new Comparator<Integer>() {
				public int compare(Integer a, Integer b)  {
					if(k[a] > k[b]) 
						return -1;
					if(k[a] < k[b])
						return 1;
					return 0;
				}
			});
			long sum = 0;
			List<Integer> list = new ArrayList<>();
			for (int i = 0; i < n; i++) {
				if(sum+k[indices[i]] <= W) {
					sum += k[indices[i]];
					list.add(indices[i]+1);
				}
			}
			if(sum >= (W + 1) / 2) {
				System.out.println(list.size());
				for (int i = 0; i < list.size(); i++)
					System.out.print(list.get(i) + " ");
				System.out.println();
			} else {
				System.out.println(-1);
			}
		}
	}

	public int[] strToIntArr(String[] arr) {
		return Stream.of(arr).mapToInt(Integer::parseInt).toArray();
	}

	public boolean deq(double a, double b) {
		return Math.abs(a - b) < 0.0001;
	}

	public double dist(double a, double b, double c, double d) {
		return Math.sqrt((a - c) * (a - c) + (b - d) * (b - d));
	}

	public boolean hasMore(String line) {
		return line != null && !line.equals("");
	}

	public int max(int a, int b, int c) {
		return Math.max(a, Math.max(b, c));
	}

	public int min(int a, int b, int c) {
		return Math.min(a, Math.min(b, c));
	}

	class Writer {
		PrintWriter output;

		public Writer(OutputStream out) {
			this.output = new PrintWriter(new OutputStreamWriter(out));
		}

		public void println(Object s) {
			output.println(s.toString());
		}

		public void print(Object s) {
			output.print(s.toString());
		}

		public void flush() {
			output.flush();
		}
	}

	class Scanner {
		BufferedReader br;
		StringTokenizer in;

		public Scanner(InputStream inputStream) {
			br = new BufferedReader(new InputStreamReader(inputStream));
		}

		public String next() {
			return hasMoreTokens() ? in.nextToken() : null;
		}

		public String readLine() {
			try {
				return br.readLine();
			} catch (Exception e) {
				e.printStackTrace();
				return null;
			}
		}

		boolean hasMoreTokens() {
			while (in == null || !in.hasMoreTokens()) {
				String s = readLine();
				if (s == null)
					return false;
				in = new StringTokenizer(s);
			}
			return true;
		}

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

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

		public double nd() {
			return Double.parseDouble(nextString());
		}

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

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

		public long[] nla(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++) {
				a[i] = ni();
			}
			return a;
		}
	}

	class Pair implements Comparable<Pair> {
		long _first, _second;

		public Pair(int f, int s) {
			_first = f;
			_second = s;
		}

		public Pair(Long f, Long s) {
			_first = f;
			_second = s;
		}

		public int compareTo(Pair o) {
			if (this.first() != o.first())
				return Long.compare(this.first(), o.first());
			else
				return Long.compare(this.second(), o.second());
		}

		long first() {
			return _first;
		}

		long second() {
			return _second;
		}

		int firsti() {
			return (int) _first;
		}

		int secondi() {
			return (int) _second;
		}
	}

	class Triple implements Comparable<Triple> {
		Integer _first, _second, _third;

		public Triple(Integer f, Integer s, Integer t) {
			_first = f;
			_second = s;
			_third = t;
		}

		public int compareTo(Triple o) {
			if (!this.first().equals(o.first()))
				return this.first() - o.first();
			else if (!this.second().equals(o.second()))
				return this.second() - o.second();
			else
				return this.third() - o.third();
		}

		Integer first() {
			return _first;
		}

		Integer second() {
			return _second;
		}

		Integer third() {
			return _third;
		}

		public String toString() {
			return first() + " " + second() + " " + third();
		}
	}

	class UnionFind {
		private ArrayList<Integer> p, rank, setSize;
		private int numSets;

		public UnionFind(int N) {
			p = new ArrayList<>(N);
			rank = new ArrayList<>(N);
			setSize = new ArrayList<>(N);
			numSets = N;
			for (int i = 0; i < N; i++) {
				p.add(i);
				rank.add(0);
				setSize.add(1);
			}
		}

		public int find(int i) {
			if (p.get(i) == i)
				return i;
			else {
				int ret = find(p.get(i));
				p.set(i, ret);
				return ret;
			}
		}

		public boolean connected(int i, int j) {
			return find(i) == find(j);
		}

		public void union(int i, int j) {
			if (!connected(i, j)) {
				numSets--;
				int x = find(i), y = find(j);
				if (rank.get(x) > rank.get(y)) {
					p.set(y, x);
					setSize.set(x, setSize.get(x) + setSize.get(y));
				} else {
					p.set(x, y);
					setSize.set(y, setSize.get(y) + setSize.get(x));
					if (rank.get(x) == rank.get(y))
						rank.set(y, rank.get(y) + 1);
				}
			}
		}

		public int numDisjointSets() {
			return numSets;
		}

		public int size(int i) {
			return setSize.get(find(i));
		}
	}

	class SegmentTree {
		private int[] st, A;
		private int n;
		private boolean min;

		public SegmentTree(int[] _A, boolean _min) {
			min = _min;
			A = _A;
			n = A.length;
			st = new int[4 * n];
			for (int i = 0; i < 4 * n; i++)
				st[i] = 0;
			build(1, 0, n - 1);
		}

		private int left(int p) {
			return p << 1;
		}

		private int right(int p) {
			return (p << 1) + 1;
		}

		private void build(int p, int L, int R) {
			if (L == R)
				st[p] = A[L]; // L
			else {
				build(left(p), L, (L + R) / 2);
				build(right(p), (L + R) / 2 + 1, R);
				int p1 = st[left(p)], p2 = st[right(p)];
				st[p] = p1 + p2; // ((min && A[p1] <= A[p2]) || (!min && A[p1] >= A[p2])) ? p1 : p2;
			}
		}

		private int rmq(int p, int L, int R, int i, int j) {
			if (i > R || j < L)
				return -1;
			if (L >= i && R <= j)
				return st[p];

			int p1 = rmq(left(p), L, (L + R) / 2, i, j);
			int p2 = rmq(right(p), (L + R) / 2 + 1, R, i, j);

			if (p1 == -1)
				return p2;
			if (p2 == -1)
				return p1;
			return p1 + p2; // ((min && A[p1] <= A[p2]) || (!min && A[p1] >= A[p2])) ? p1 : p2;
		}

		private int update_point(int p, int L, int R, int idx, int new_value) {
			int i = idx, j = idx;

			if (i > R || j < L)
				return st[p];

			if (L == i && R == j) {
				A[i] = new_value;
				return st[p] = A[L];
			}

			int p1, p2;
			p1 = update_point(left(p), L, (L + R) / 2, idx, new_value);
			p2 = update_point(right(p), (L + R) / 2 + 1, R, idx, new_value);
			return st[p] = p1 + p2; // ((min && A[p1] <= A[p2]) || (!min && A[p1] >= A[p2])) ? p1 : p2;
		}

		public int rmq(int i, int j) {
			return rmq(1, 0, n - 1, i, j);
		}

		public int update_point(int idx, int new_value) {
			return update_point(1, 0, n - 1, idx, new_value);
		}
	}

}