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.util.*;
import java.lang.Math;
import java.util.concurrent.TimeUnit;
import java.util.stream.Collectors;
import java.io.*;
import java.math.BigInteger;
import java.io.FileWriter;

public class CodeForces2 {

	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 FastReader f = new FastReader();

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

	static void print(boolean s) {
		System.out.print(s);
	}

	static ArrayList<Long> sieveOfEratosthenes(int n) {
		// Create a boolean array "prime[0..n]" and initialize
		// all entries it as true. A value in prime[i] will
		// finally be false if i is Not a prime, else true.
		boolean prime[] = new boolean[n + 1];
		for (int i = 0; i < n; i++)
			prime[i] = true;

		for (int p = 2; p * p <= n; p++) {
			// If prime[p] is not changed, then it is a prime
			if (prime[p] == true) {
				// Update all multiples of p
				for (int i = p * p; i <= n; i += p)
					prime[i] = false;
			}
		}
		ArrayList<Long> arr = new ArrayList<>();
		// Print all prime numbers
		for (int i = 2; i <= n; i++) {
			if (prime[i] == true)
				arr.add((long) i);
		}
		return arr;
	}

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

		// This is checked so that we can skip
		// middle five numbers in below loop
		if (n % 2 == 0 || n % 3 == 0)
			return false;

		for (int i = 5; i * i <= n; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;

		return true;
	}

	static long[] inArr(long a[], int n) {
		for (int i = 0; i < n; i++)
			a[i] = f.nextLong();
		return (a);
	}

	static void printSubsets(int set[]) {
		int n = set.length;
		Arrays.sort(set);
		for (int i = 0; i < n; i++) {

		}
		HashMap<Integer, Integer> hm = new HashMap<>();
		for (int i = 0; i < (1 << n); i++) {
			for (int j = 0; j < n; j++) {
				if ((i & (1 << j)) > 0) {
					if (hm.get(set[j]) == null) {
						hm.put(set[j], 0);
					}
					hm.put(set[j], hm.get(set[j]) + 1);

				}
			}

		}
	}

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

	static long lcm(long a, long b) {
		return (a * b) / gcd(a, b);
	}

	static long power(long x, long y, long p) {

		// Initialize result
		long res = 1;

		// Update x if it is more than or
		// equal to p
		x = x % p;

		while (y > 0) {

			// If y is odd, multiply x
			// with result
			if (y % 2 == 1)
				res = (res * x) % p;

			// y must be even now
			y = y >> 1; // y = y/2
			x = (x * x) % p;
		}

		return res;
	}

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

	static long nCrModPFermat(int n, int r) {
		long p = 1000000007;

		// Base case
		if (r == 0)
			return 1;

		// Fill factorial array so that we
		// can find all factorial of r, n
		// and n-r
		long[] fac = new long[n + 1];
		fac[0] = 1;

		for (int i = 1; i <= n; i++)
			fac[i] = fac[i - 1] * i % p;

		return (fac[n] * modInverse(fac[r], p) % p * modInverse(fac[n - r], p) % p) % p;
	}

	static int solve(int a[], int n, int N, int dp[]) {
		if (dp[n] != -1) {
			return dp[n];
		}

		dp[n] = a[n] + ((n + a[n] >= N) ? 0 : solve(a, n + a[n], N, dp));
		return dp[n];

	}

	/* =============================CODE======================= */
	public static void main(String args[]) throws Exception {
		BufferedWriter w = new BufferedWriter(new OutputStreamWriter(System.out));
		// Random rand = new Random();
		int t = f.nextInt();
		while (t-- != 0) {
			int n = f.nextInt();
			long wt = f.nextLong();
			// System.out.println("n="+n+"wt="+wt);
			long wi[] = new long[n];
			
			long c = -1;
			int pos = 0;
			for (int i = 0; i < n; i++) {
				// System.out.println('f');
				wi[i] = f.nextLong();
				if (wi[i] > wt) {
					wi[i] = -1;
					continue;
				}
				if (wi[i] >= (wt + 1) / 2 && wi[i] <= wt) {
					c = wi[i];
					pos = i;
					// break;
				}
			}
			if (c != -1) {
				w.write("1\n" + (pos + 1) + "\n");
			} else {
				c = 0;
				ArrayList<Integer> arr = new ArrayList<>();
				for (int i = 0; i < n; i++) {
					if (wi[i] != -1 && c + wi[i] <= wt) {
						c += wi[i];
						arr.add(i);
					}
				}
				if (c >= (wt + 1) / 2 && c <= wt) {
				w.write(arr.size() + "\n");
					for (int i = 0; i < arr.size(); i++) {
						w.write((arr.get(i) + 1) + " ");
					}
					w.write("\n");
				} else {
					w.write("-1\n");
				}
			}
			// w.write("fuck\n");
		}
		w.flush();
	}
}
// 1 1
// 1
// 1 1
// 2
// 2 1
// 2 1
// 1 1
// 3
// 2 1
// 1 3
// 2 1
// 3 2