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.math.*;
import java.util.*;

public class test {

	static int INF = 1000000007;

	public static void main(String[] args) {
		int test = fs.nextInt();
//		int test = 1;
		for (int cases = 0; cases < test; cases++) {
			int n = fs.nextInt();
			long w = fs.nextLong();
			long m = (long) Math.ceil((double) w / 2);
			LongPair ar[] = new LongPair[n];
			long sum = 0;
			for (int i = 0; i < ar.length; i++) {
				ar[i] = new LongPair(fs.nextLong(), i + 1);
			}
			boolean rs = false;
			Arrays.sort(ar, new Comparator<LongPair>() {

				@Override
				public int compare(LongPair o1, LongPair o2) {
					// TODO Auto-generated method stub
					return (int) (o1.first - o2.first);
				}
			});
//			for (LongPair longPair : ar) {
//				System.out.println(longPair.first + " " + longPair.second);
//			}
			ArrayList<Long> s = new ArrayList<Long>();
			int i = n - 1;
			for (; i >= 0; i--) {
				if (ar[i].first >= m && ar[i].first <= w) {
					rs = true;
					s.add(ar[i].second);
					break;
				} else if (ar[i].first > w) {
					continue;
				} else {
					break;
				}
			}
			if (!rs) {
				for (int j = i; j >= 0; j--) {
					if (sum + ar[j].first >= m && sum + ar[j].first <= w) {
						sum += ar[j].first;
						s.add(ar[j].second);
						rs = true;
						break;
					} else if (sum + ar[j].first < m) {
						sum += ar[j].first;
						s.add(ar[j].second);
					}
				}
			}
			if (!rs) {
				System.out.println(-1);
			} else {
				System.out.println(s.size());
				for (Long long1 : s) {
					System.out.print(long1 + " ");
				}
				System.out.println();
			}

		}

	}

	static boolean isSubSequence(String str1, String str2, int m, int n) {
		if (m == 0)
			return true;
		if (n == 0)
			return false;
		if (str1.charAt(m - 1) == str2.charAt(n - 1))
			return isSubSequence(str1, str2, m - 1, n - 1);
		return isSubSequence(str1, str2, m, n - 1);
	}

	static long power(long x, long y, long p) {
		long res = 1;
		x = x % p;
		while (y > 0) {
			if (y % 2 == 1)
				res = (res * x) % p;
			y = y >> 1;
			x = (x * x) % p;
		}
		return res;
	}

	static long modInverse(long n, long p) {
		return power(n, p - 2, p);
	}

	static long nCrModPFermat(long n, long r, long p) {
		long ans1 = 1;
		long i = n;
		long k = r;
		while (k > 0) {
			ans1 = mul(ans1, i, p);
			i--;
			k--;
		}
		long ans2 = 1;
		while (r > 0) {
			ans2 = mul(ans2, r, p);
			r--;
		}
		r = modInverse(ans2, p);
		ans1 = mul(ans1, r, p);
		return ans1;
	}

	static long facCalc(long total) {
		long ans = 1;
		for (long i = 2; i <= total; i++) {
			ans = mul(ans, i, INF);
		}
		return ans;
	}

	static long mul(long a, long b, long p) {
		return ((a % p) * (b % p)) % p;
	}

	static void sieve() {
		boolean prime[] = new boolean[101];
		Arrays.fill(prime, true);
		prime[1] = false;
		for (int i = 2; i * i <= prime.length - 1; i++) {
			for (int j = i * i; j <= prime.length - 1; j += i) {
				prime[j] = false;
			}
		}
	}

	public static int[] radixSort(int[] f) {
		return radixSort(f, f.length);
	}

	public static int[] radixSort(int[] f, int n) {
		int[] to = new int[n];
		{
			int[] b = new int[65537];
			for (int i = 0; i < n; i++)
				b[1 + (f[i] & 0xffff)]++;
			for (int i = 1; i <= 65536; i++)
				b[i] += b[i - 1];
			for (int i = 0; i < n; i++)
				to[b[f[i] & 0xffff]++] = f[i];
			int[] d = f;
			f = to;
			to = d;
		}
		{
			int[] b = new int[65537];
			for (int i = 0; i < n; i++)
				b[1 + (f[i] >>> 16)]++;
			for (int i = 1; i <= 65536; i++)
				b[i] += b[i - 1];
			for (int i = 0; i < n; i++)
				to[b[f[i] >>> 16]++] = f[i];
			int[] d = f;
			f = to;
			to = d;
		}
		return f;
	}

	static void printArray(int ar[]) {
		System.out.println(Arrays.toString(ar));
	}

	static class Pair {
		int first, second;

		public Pair(int first, int second) {
			this.first = first;
			this.second = second;
		}

	}

	static class LongPair {
		long first;
		long second;

		LongPair(long a, long b) {
			this.first = a;
			this.second = b;
		}

	}

	static long expmodulo(long a, long b, long c) {
		long x = 1;
		long y = a;
		while (b > 0) {
			if (b % 2 == 1) {
				x = (x * y) % c;
			}
			y = (y * y) % c; // squaring the base
			b /= 2;
		}
		return (long) x % c;
	}

	// static int modInverse(int a, int m) {
	// int m0 = m;
	// int y = 0, x = 1;
	//
	// if (m == 1)
	// return 0;
	//
	// while (a > 1) {
	// int q = a / m;
	// int t = m;
	// m = a % m;
	// a = t;
	// t = y;
	// y = x - q * y;
	// x = t;
	// }
	// if (x < 0)
	// x += m0;
	// return x;
	// }

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

	static void sortMyMapusingValues(HashMap<Integer, Integer> hm) {

		List<Map.Entry<Integer, Integer>> capitalList = new LinkedList<>(hm.entrySet());

		Collections.sort(capitalList, new Comparator<Map.Entry<Integer, Integer>>() {
			public int compare(Map.Entry<Integer, Integer> o1, Map.Entry<Integer, Integer> o2) {
				return (o1.getValue()).compareTo(o2.getValue());
			}
		});
		HashMap<Integer, Integer> result = new HashMap<>();
		for (Map.Entry<Integer, Integer> entry : capitalList) {
			result.put(entry.getKey(), entry.getValue());
		}
	}

	static boolean ispowerof2(long num) {
		if ((num & (num - 1)) == 0)
			return true;
		return false;
	}

	static void primeFactors(int n) {
		while (n % 2 == 0) {
			System.out.print(2 + " ");
			n /= 2;
		}
		for (int i = 3; i <= Math.sqrt(n); i += 2) {
			while (n % i == 0) {
				System.out.print(i + " ");
				n /= i;
			}
		}
		if (n > 2)
			System.out.print(n);
	}

	static boolean isPrime(long n) {
		// Corner cases
		if (n <= 1)
			return false;
		if (n <= 3)
			return true;
		if (n % 2 == 0 || n % 3 == 0)
			return false;

		long sq = (long) Math.sqrt(n);
		for (int i = 5; i <= sq; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;

		return true;
	}

	static class Graph {
		HashMap<Integer, LinkedList<Integer>> hm = new HashMap<Integer, LinkedList<Integer>>();

		private void addVertex(int vertex) {
			hm.put(vertex, new LinkedList<>());
		}

		private void addEdge(int source, int dest, boolean bi) {
			if (!hm.containsKey(source))
				addVertex(source);
			if (!hm.containsKey(dest))
				addVertex(dest);
			hm.get(source).add(dest);
			if (bi) {
				hm.get(dest).add(source);
			}
		}

		private boolean uniCycle(int i, HashSet<Integer> visited, int parent) {
			visited.add(i);
			LinkedList<Integer> list = hm.get(i);
			Iterator<Integer> it = list.iterator();
			while (it.hasNext()) {
				Integer integer = (Integer) it.next();
				if (!visited.contains(integer)) {
					if (uniCycle(integer, visited, i))
						return true;
				} else if (integer != parent) {
					return true;
				}
			}
			return false;
		}

		private boolean uniCyclic() {
			HashSet<Integer> visited = new HashSet<Integer>();
			Set<Integer> set = hm.keySet();
			for (Integer integer : set) {
				if (!visited.contains(integer)) {
					if (uniCycle(integer, visited, -1)) {
						return true;
					}
				}
			}
			return false;
		}

		private boolean isbiCycle(int i, HashSet<Integer> visited, HashSet<Integer> countered) {
			if (countered.contains(i))
				return true;
			if (visited.contains(i))
				return false;
			visited.add(i);
			countered.add(i);
			LinkedList<Integer> list = hm.get(i);
			Iterator<Integer> it = list.iterator();
			while (it.hasNext()) {
				Integer integer = (Integer) it.next();
				if (isbiCycle(integer, visited, countered)) {
					return true;
				}
			}
			countered.remove(i);
			return false;
		}

		Boolean isReachable(int s, int d, int k) {
			if (hm.isEmpty()) {
				return false;
			}
			LinkedList<Integer> temp;
			boolean visited[] = new boolean[k];
			LinkedList<Integer> queue = new LinkedList<Integer>();
			visited[s] = true;
			queue.add(s);
			Iterator<Integer> i;
			while (queue.size() != 0) {
				s = queue.poll();
				int n;
				i = hm.get(s).listIterator();

				// Get all adjacent vertices of the dequeued vertex s
				// If a adjacent has not been visited, then mark it
				// visited and enqueue it
				while (i.hasNext()) {
					n = i.next();

					// If this adjacent node is the destination node,
					// then return true
					if (n == d)
						return true;

					// Else, continue to do BFS
					if (!visited[n]) {
						visited[n] = true;
						queue.add(n);
					}
				}
			}

			// If BFS is complete without visited d
			return false;
		}

		private boolean isbiCyclic() {
			HashSet<Integer> visited = new HashSet<Integer>();
			HashSet<Integer> countered = new HashSet<Integer>();
			Set<Integer> set = hm.keySet();
			for (Integer integer : set) {
				if (isbiCycle(integer, visited, countered)) {
					return true;
				}
			}
			return false;
		}
	}

	static class Node {
		Node left, right;
		int data;

		public Node(int data) {
			this.data = data;
		}

		public void insert(int val) {
			if (val <= data) {
				if (left == null) {
					left = new Node(val);
				} else {
					left.insert(val);
				}
			} else {
				if (right == null) {
					right = new Node(val);
				} else {
					right.insert(val);
				}
			}
		}

		public boolean contains(int val) {
			if (data == val) {
				return true;
			} else if (val < data) {
				if (left == null) {
					return false;
				} else {
					return left.contains(val);
				}
			} else {
				if (right == null) {
					return false;
				} else {
					return right.contains(val);
				}
			}
		}

		public void inorder() {
			if (left != null) {
				left.inorder();
			}
			System.out.print(data + " ");
			if (right != null) {
				right.inorder();
			}
		}

		public int maxDepth() {
			if (left == null)
				return 0;
			if (right == null)
				return 0;
			else {
				int ll = left.maxDepth();
				int rr = right.maxDepth();
				if (ll > rr)
					return (ll + 1);
				else
					return (rr + 1);
			}
		}

		public int countNodes() {
			if (left == null)
				return 1;
			if (right == null)
				return 1;
			else {
				return left.countNodes() + right.countNodes() + 1;
			}
		}

		public void preorder() {
			System.out.print(data + " ");
			if (left != null) {
				left.inorder();
			}

			if (right != null) {
				right.inorder();
			}

		}

		public void postorder() {
			if (left != null) {
				left.inorder();
			}

			if (right != null) {
				right.inorder();
			}
			System.out.print(data + " ");

		}

		public void levelorder(Node node) {
			LinkedList<Node> ll = new LinkedList<Node>();
			ll.add(node);
			getorder(ll);

		}

		public void getorder(LinkedList<Node> ll) {
			while (!ll.isEmpty()) {
				Node node = ll.poll();
				System.out.print(node.data + " ");
				if (node.left != null)
					ll.add(node.left);
				if (node.right != null)
					ll.add(node.right);
			}
		}
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

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

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

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

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	static class OutputWriter {
		private final PrintWriter writer;

		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}

		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}

		public void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}

		public void printLine(Object... objects) {
			print(objects);
			writer.println();
		}

		public void close() {
			writer.close();
		}

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

	}

	private static final FastReader fs = new FastReader();
	private static final OutputWriter op = new OutputWriter(System.out);
}