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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.*;

public class C {
	private static final FastReader fs = new FastReader();
	private static final PrintWriter out = new PrintWriter(System.out);
	
	static class Item{
		int id;long weight;
		Item(int id,long weight){
			this.id = id;
			this.weight = weight;
		}
	}

	private static void solve() {
		int n = fs.nextInt();
		long w = fs.nextLong();
		ArrayList<Item> lessThanHalf = new ArrayList<>();
		Item onlyOne = null;
		for(int i = 1; i<=n; i++) {
			long we = fs.nextLong();
			if(we > w)
				continue;
			if(we >= (w+1)/2) {
				onlyOne = new Item(i,we);
			}
			else
				lessThanHalf.add(new Item(i,we));
		}
		if(onlyOne!=null)
			out.println(1 + "\n" + onlyOne.id);
		else {
			long sum = 0;
			ArrayList<Integer> ans = new ArrayList<Integer>();
			for(int i = 0; i<lessThanHalf.size() && sum + lessThanHalf.get(i).weight < w; i++) {
				sum += lessThanHalf.get(i).weight;
				ans.add(lessThanHalf.get(i).id);
			}
			if(sum >= (w+1)/2 && sum <= w) {
				out.println(ans.size());
				for(int x : ans)
					out.print(x +" ");
				out.println();
			}
			else
				out.println(-1);
		}
	}

	public static void main(String[] args) {
		Thread t = new Thread(null, null, "", 1 << 28) {
			public void run() {
				int test_case = 1;
				test_case = fs.nextInt();
				for (int cs = 1; cs <= test_case; cs++) {
					solve();
				}
				out.close();
			}
		};
		t.start();
		try {
			t.join();
		} catch (InterruptedException e) {
			e.printStackTrace();
		}
	}

	private 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;
		}

		int[] readintarray(int n) {
			int res[] = new int[n];
			for (int i = 0; i < n; i++)
				res[i] = nextInt();
			return res;
		}

		long[] readlongarray(int n) {
			long res[] = new long[n];
			for (int i = 0; i < n; i++)
				res[i] = nextLong();
			return res;
		}
	}

	private static class cf {
		public static int min(int x, int y) {
			return Math.min(x, y);
		}

		public static int max(int x, int y) {
			return Math.max(x, y);
		}

		public static long min(long x, long y) {
			return Math.min(x, y);
		}

		public static long max(long x, long y) {
			return Math.max(x, y);
		}

		public static int abs(int x) {
			return x >= 0 ? x : -x;
		}

		public static long abs(long x) {
			return x >= 0 ? x : -x;
		}

		public static boolean even(int x) {
			return x % 2 == 0 ? true : false;
		}

		public static boolean even(long x) {
			return x % 2 == 0 ? true : false;
		}

		public static int power(int base, int exponent) {
			int res = 1;
			while (exponent > 0) {
				if (!even(exponent))
					res *= base;
				exponent >>= 1;
				base *= base;
			}
			return res;
		}

		public static long power(long base, long exponent) {
			long res = 1;
			while (exponent > 0) {
				if (!even(exponent))
					res *= base;
				exponent >>= 1;
				base *= base;
			}
			return res;
		}

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

		public static long add(long a, long b, long mod) {
			return (a % mod + b % mod) % mod;
		}

		public static long sub(long a, long b, long mod) {
			return ((a % mod - b % mod) % mod + mod) % mod;
		}

		public static long power(long base, long exponent, long mod) {
			long res = 1;
			base %= mod;
			while (exponent > 0) {
				if (!even(exponent))
					res = mul(res, base, mod);
				exponent >>= 1;
				base = mul(base, base, mod);
			}
			return res;
		}
	}
}