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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.InputMismatchException;
import java.util.List;
import java.util.StringJoiner;
import java.util.stream.IntStream;

public class C {

  public static void main(String[] args) {
    Print print = new Print();
    Scan scan = new Scan();

    int tests = scan.scanInt();
    IntStream.range(0, tests).forEach(test -> {
      int num = scan.scanInt();
      long W = Long.parseLong(scan.scanString());
      List<Point> data = new ArrayList<>();

      for (int i = 0; i < num; i++) {
        int r = scan.scanInt();
        data.add(new Point(r, i));
      }

      data.sort(Comparator.comparingInt(p1 -> p1.value));

      long bag = 0;
      boolean found = false;
      StringJoiner sj = new StringJoiner(" ");
      int count = 0;

      for (int j = data.size() - 1; j >= 0; j--) {
        if (bag + data.get(j).value > W) {
        } else {
          bag += data.get(j).value;
          count++;
          sj.add(Integer.toString(data.get(j).index));
          if (bag >= ((W + 1) / 2)) {
            found = true;
            break;
          }
        }
      }

      if (found) {
        print.printLine(Integer.toString(count));
        print.printLine(sj.toString());
      } else {
        print.printLine("-1");
      }
    });

    print.close();

  }

  static class Scan {

    private byte[] buf = new byte[1024];
    private int index;
    private InputStream in;
    private int total;

    public Scan() {
      in = System.in;
    }

    public int scan() {
      if (total < 0) {
        throw new InputMismatchException();
      }
      if (index >= total) {
        index = 0;
        try {
          total = in.read(buf);
        } catch (IOException ignored) {
        }
        if (total <= 0) {
          return -1;
        }
      }
      return buf[index++];
    }

    public int scanInt() {
      int integer = 0;
      int n = scan();
      while (isWhiteSpace(n)) {
        n = scan();
      }
      int neg = 1;
      if (n == '-') {
        neg = -1;
        n = scan();
      }
      while (!isWhiteSpace(n)) {
        if (n >= '0' && n <= '9') {
          integer *= 10;
          integer += n - '0';
          n = scan();
        } else {
          throw new InputMismatchException();
        }
      }
      return neg * integer;
    }

    public double scanDouble() {
      double doub = 0;
      int n = scan();
      while (isWhiteSpace(n)) {
        n = scan();
      }
      int neg = 1;
      if (n == '-') {
        neg = -1;
        n = scan();
      }
      while (!isWhiteSpace(n) && n != '.') {
        if (n >= '0' && n <= '9') {
          doub *= 10;
          doub += n - '0';
          n = scan();
        } else {
          throw new InputMismatchException();
        }
      }
      if (n == '.') {
        n = scan();
        double temp = 1;
        while (!isWhiteSpace(n)) {
          if (n >= '0' && n <= '9') {
            temp /= 10;
            doub += (n - '0') * temp;
            n = scan();
          } else {
            throw new InputMismatchException();
          }
        }
      }
      return doub * neg;
    }

    public String scanString() {
      StringBuilder sb = new StringBuilder();
      int n = scan();
      while (isWhiteSpace(n)) {
        n = scan();
      }
      while (!isWhiteSpace(n)) {
        sb.append((char) n);
        n = scan();
      }
      return sb.toString();
    }

    private boolean isWhiteSpace(int n) {
      if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) {
        return true;
      }
      return false;
    }
  }

  static class Print {

    private final BufferedWriter bw;

    public Print() {
      bw = new BufferedWriter(new OutputStreamWriter(System.out));
    }

    public void print(String str) {
      try {
        bw.append(str);
      } catch (IOException ignored) {
      }
    }

    public void printLine(String str) {
      print(str);
      try {
        bw.append("\n");
      } catch (IOException ignored) {
      }
    }

    public void close() {
      try {
        bw.close();
      } catch (IOException ignored) {
      }
    }
  }

  static class Point {

    private int value;
    private int index;

    public Point(int value, int index) {
      this.value = value;
      this.index = index + 1;
    }
  }

}