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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.sql.Timestamp;
import java.time.LocalDate;
import java.time.LocalDateTime;
import java.time.ZoneOffset;
import java.time.format.DateTimeFormatter;
import java.util.*;
import java.util.Map.Entry;
import java.util.concurrent.atomic.AtomicInteger;
import java.util.stream.IntStream;
import java.util.stream.Stream;


/**
 * for competitive programming
 * @author BrolyCode
 * @version 1.0.0
 */

public class CP {

    static Random random;

    private static void mySort(int[] s) {
        for (int i = 0; i < s.length; ++i) {
            int j = random.nextInt(i + 1);
            int t = s[i];
            s[i] = s[j];
            s[j] = t;
        }
        Arrays.sort(s);
    }

    static class Pair<A,B>{
        A x;
        B y;

        public Pair(A x, B y) {
            this.x=x;
            this.y=y;
        }

    }

    public static void pairSort(Pair[] p,  Comparator<? super Pair> c) {
        Arrays.sort(p, c);
    }
    
    static class Trie {
        Map<Character,Trie> children;
        boolean end;
        
        public Trie() {
            children = new HashMap<>();
        }
    }
    
    private static void insert(String s, Trie node) {
        insertRec(s, node, 0);
    }
    
    public static void insertRec(String s, Trie node, int index) {
        if(index == s.length()){
            node.end = true;
        }else if(node.children.containsKey(s.charAt(index))) {
            insertRec(s, node.children.get(s.charAt(index)), index + 1);
        } else {
            node.children.put(s.charAt(index),new Trie());
            insertRec(s, node.children.get(s.charAt(index)), index + 1);
        }
    }
    
    private static int contains(String s, Trie node) {
        return containsRec(s, node, 0);
    }
    
    public static int containsRec(String s, Trie node, int index) {
        if(index == s.length() && node.end == true)
            return 0;
        else if(index == s.length())
            return 1;
        else if(node.children.containsKey(s.charAt(index))) {
            return containsRec(s, node.children.get(s.charAt(index)), index + 1);
        } else
            return -1;
    }

    public static void main(String[] args) {
        random = new Random(543534151132L + System.currentTimeMillis());
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        task(in,out);
        out.close();
    }

    private static void task(InputReader in, PrintWriter out) {
    
//        int n = in.nextInt();
//        int m = in.nextInt();
//        String A = in.next();
//        String B = in.next();
//
//        int[][] dp = new int[n + 1][m + 1];
//        int ans = 0;
//
//        for(int i = 1; i <= n; i++) {
//            for(int j = 1; j <= m; j++) {
//                if(A.charAt(i - 1) == B.charAt(j - 1))
//                    dp[i][j] = dp[i - 1][j - 1] + 2;
//                else
//                    dp[i][j] = Math.max(0, Math.max(dp[i - 1][j], dp[i][j - 1]) - 1);
//                ans = Math.max(ans, dp[i][j]);
//            }
//        }
//
//        out.println(ans);
        
        
        
        int t = in.nextInt();
        while(--t >= 0) {
            int n = in.nextInt();
            long W = in.nextLong();
            
            long c = (long) Math.ceil(W / 2.);
            
            int[][] T = new int[n][2];
            
            for(int i = 0; i < n; i++) {
                T[i][0] = in.nextInt();
                T[i][1] = i + 1;
            }
            
            Arrays.sort(T, (a,b) -> a[0] - b[0]);
            
            int l = 0;
            int r = n - 1;
            long sum = 0;
            for(int[] x : T)
                sum += x[0];
            
            boolean ok = false;
            
            while(l <= r && !ok) {
                if(sum >= c && sum <= W)
                    ok = true;
                else if(sum - T[r][0] >= c) {
                    sum -= T[r--][0];
                }
                else {
                    sum -= T[l++][0];
                }
            }
            
            if(ok) {
                out.println(r - l + 1);
                for(int i = l; i <= r; i++)
                    out.print(T[i][1] + " ");
                out.println();
            } else {
                out.println(-1);
            }
        }
    
    }
    
    public static int find(int[] T, int x) {
        if(x == T[x])
            return x;
        return find(T,T[x]);
    }
    
    public static void add(int[] T, int a, int b) {
        T[b] = find(T, a);
    }
    
    public static int gcd(int a, int b)
    {
        BigInteger b1 = BigInteger.valueOf(a);
        BigInteger b2 = BigInteger.valueOf(b);
        BigInteger gcd = b1.gcd(b2);
        return gcd.intValue();
    }

    public static long gcd(long a, long b)
    {
        BigInteger b1 = BigInteger.valueOf(a);
        BigInteger b2 = BigInteger.valueOf(b);
        BigInteger gcd = b1.gcd(b2);
        return gcd.longValue();
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

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

        public float nextFloat() {
            return Float.parseFloat(next());
        }

    }

}