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.BufferedInputStream;
import java.io.IOException;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileInputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Arrays;

/**
 *
 * @author meimarcel
 */
public class C683 {
    class Pair implements Comparable<Pair>{
        public int id;
        public int num;
        public Pair(int id, int num) {
            this.id = id;
            this.num = num;
        }

        @Override
        public int compareTo(Pair p) {
            return this.num - p.num;
        }
    }
    public void run() throws IOException {
        int t = in.nextInt();
        while(t-- > 0) {
            int n = in.nextInt();
            long w = in.nextLong();
            long meio = (long) Math.ceil(w/2.0);
            Pair nums[] = new Pair[n];
            int m = 0;
            StringBuilder res = new StringBuilder();
            boolean can[] = new boolean[n]; 
            for(int i = 0 ; i < n; ++i) {
                int we = in.nextInt();
                if(we >= meio && we <= w) {
                    m = 1;
                    res = new StringBuilder();
                    res.append(i+1);
                }
                nums[i] = new Pair(i, we);
            }
            if(m > 0) {
                out.println(m);
                out.println(res);
            } else {
                Arrays.sort(nums);
                boolean find = false;
                long total = 0;
                for(int i = 0; i < n; ++i) {
                    total += nums[i].num;
                    can[nums[i].id] = true;
                    m++;
                    if(total >= meio && total <= w) {
                        find = true;
                        break;
                    }
                    int index = i;
                    while(total > w) {
                        m--;
                        total -= nums[index].num;
                        can[nums[index].id] = false;
                        index--;
                    }
                }
                if(find) {
                    out.println(m);
                    for(int i = 0; i < n; ++i) {
                        if(can[i]) {
                            res.append(" "+(i+1));
                        }
                    }
                    out.println(res.toString().trim());
                } else {
                    out.println(-1);
                }
            }
            
        }
        out.flush();
    }

    public static void main(String[] args) throws IOException {
        new C683().run();
    }
    
    FastScanner in = new FastScanner();
    PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    
    class FastScanner {
        private int BS = 1 << 16;
        private char NC = (char) 0;
        private byte[] buf = new byte[BS];
        private int bId = 0, size = 0;
        private char c = NC;
        private double cnt = 1;
        private BufferedInputStream in;
 
        public FastScanner() {
            in = new BufferedInputStream(System.in, BS);
        }
 
        public FastScanner(String s) {
            try {
                in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
            } catch (Exception e) {
                in = new BufferedInputStream(System.in, BS);
            }
        }
 
        private char getChar() {
            while (bId == size) {
                try {
                    size = in.read(buf);
                } catch (Exception e) {
                    return NC;
                }
                if (size == -1) return NC;
                bId = 0;
            }
            return (char) buf[bId++];
        }
 
        public int nextInt() {
            return (int) nextLong();
        }
 
        public int[] nextInts(int N) {
            int[] res = new int[N];
            for (int i = 0; i < N; i++) {
                res[i] = (int) nextLong();
            }
            return res;
        }
 
        public long[] nextLongs(int N) {
            long[] res = new long[N];
            for (int i = 0; i < N; i++) {
                res[i] = nextLong();
            }
            return res;
        }
 
        public long nextLong() {
            cnt = 1;
            boolean neg = false;
            if (c == NC) c = getChar();
            for (; (c < '0' || c > '9'); c = getChar()) {
                if (c == '-') neg = true;
            }
            long res = 0;
            for (; c >= '0' && c <= '9'; c = getChar()) {
                res = (res << 3) + (res << 1) + c - '0';
                cnt *= 10;
            }
            return neg ? -res : res;
        }
 
        public double nextDouble() {
            double cur = nextLong();
            return c != '.' ? cur : cur + nextLong() / cnt;
        }
 
        public double[] nextDoubles(int N) {
            double[] res = new double[N];
            for (int i = 0; i < N; i++) {
                res[i] = nextDouble();
            }
            return res;
        }
 
        public String next() {
            StringBuilder res = new StringBuilder();
            while (c <= 32) c = getChar();
            while (c > 32) {
                res.append(c);
                c = getChar();
            }
            return res.toString();
        }
 
        public String nextLine() {
            StringBuilder res = new StringBuilder();
            while (c <= 32) c = getChar();
            while (c != '\n') {
                res.append(c);
                c = getChar();
            }
            return res.toString();
        }
 
        public boolean hasNext() {
            if (c > 32) return true;
            while (true) {
                c = getChar();
                if (c == NC) return false;
                else if (c > 32) return true;
            }
        }
    }
    
}