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:
// package eround101;

import java.util.*;
import java.io.*;
import java.lang.*;
import java.util.StringTokenizer;

public class C101 {

    static HritikScanner sc = new HritikScanner();
    static PrintWriter pw = new PrintWriter(System.out, true);
    final static int MOD = (int) (1e9 + 7);
    static int[] count = new int[1000001];
    static StringBuilder sb = new StringBuilder();

    public static void main(String[] args) {

        int t = sc.nextInt();
        while (t-- > 0) {
            solve();
        }
    }

    static void solve(){
        int n = ni();
        long W = nl();
        ArrayList<Pair> list = new ArrayList<>();
        for(int i = 1; i <= n; i++)
        {
            list.add(new Pair(ni(), i));
        }
        Collections.sort(list);
//        for(Pair ele : list)
//        {
//            p(ele.get1()+" ");
//        }
        long sum = 0;
        long base = W/2 + (W%2 == 0 ? 0:1);
//        pl("base = " + base);
        ArrayList<Integer> index = new ArrayList<>();
        for(int i = 0; i < n; i++)
        {
            if(list.get(i).get1() >= base && list.get(i).get1() <= W )
            {
                pl(1);
                pl(list.get(i).get2());
                return;
            }
        }
        
        for(int i = 0; i < n; i++)
        {
            sum += list.get(i).get1();
            index.add(list.get(i).get2());
            if(base <= sum && sum <= W)
            {
                break;
            }
            if(sum > W)
            {
                pl(-1);
                return;
            }
        }
        if(base > sum)
        {
            pl(-1);
            return;
        }
        else
        {
            pl(index.size());
            pa(index);
        }
        
    }

    /////////////////////////////////////////////////////////////////////////////////
    
    static int[] nextIntArray(int n){
		int[] arr= new int[n];
		int i=0;
		while(i<n){
			arr[i++]=ni();
		}
		return arr;
	}
	static int[] nextIntArray1(int n){
		int[] arr= new int[n+1];
		int i=1;
		while(i<=n){
			arr[i++]= ni();
		}
		return arr;
	}
    /////////////////////////////////////////////////////////////////////////////////
    static int ni() {
        return sc.nextInt();
    }

    static long nl() {
        return sc.nextLong();
    }

    static double nd() {
        return sc.nextDouble();
    }

    /////////////////////////////////////////////////////////////////////////////////
    static void pl() {
        pw.println();
    }

    static void p(Object o) {
        pw.print(o+" ");
    }

    static void pl(Object o) {
        pw.println(o);
    }

    static void psb(StringBuilder sb) {
        pw.print(sb);
    }

    static void pa(Object arr[]) {
        for (Object o : arr) {
            p(o);
        }
        pl();
    }

    static void pa(int arr[]) {
        for (int o : arr) {
            p(o);
        }
        pl();
    }

    static void pa(long arr[]) {
        for (long o : arr) {
            p(o);
        }
        pl();
    }

    static void pa(double arr[]) {
        for (double o : arr) {
            p(o);
        }
        pl();
    }

    static void pa(char arr[]) {
        for (char o : arr) {
            p(o);
        }
        pl();
    }

    static void pa(List list) {
        for (Object o : list) {
            p(o);
        }
        pl();
    }

    static void pa(Object[][] arr) {

        for (int i = 0; i < arr.length; ++i) {
            for (Object o : arr[i]) {
                p(o);
            }
            pl();
        }
    }

    static void pa(int[][] arr) {
        for (int i = 0; i < arr.length; ++i) {
            for (int o : arr[i]) {
                p(o);
            }
            pl();
        }
    }

    static void pa(long[][] arr) {
        for (int i = 0; i < arr.length; ++i) {
            for (long o : arr[i]) {
                p(o);
            }
            pl();
        }
    }

    static void pa(char[][] arr) {
        for (int i = 0; i < arr.length; ++i) {
            for (char o : arr[i]) {
                p(o);
            }
            pl();
        }
    }

    static void pa(double[][] arr) {
        for (int i = 0; i < arr.length; ++i) {
            for (double o : arr[i]) {
                p(o);
            }
            pl();
        }
    }

/////////////////////////////////////////////////////////////////////////////////
    static void print(Object s) {
        System.out.println(s);
    }

    /////////////////////////////////////////////////////////////////////////////////
    //-----------HritikScanner class for faster input----------//
    static class HritikScanner {

        BufferedReader br;
        StringTokenizer st;

        public HritikScanner() {
            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;
        }
    }

    //////////////////////////////////////////////////////////////////
    public static class Pair implements Comparable<Pair> {

        int h, w;

        Pair(int h, int w) {
            this.h = h;
            this.w = w;

        }
        
        public int get1()
        {
            return h;
        }
        public int get2()
        {
            return w;
        }
                

        public int compareTo(Pair A) {
            return this.h - A.h;
        }
    }

    //////////////////////////////////////////////////////////////////
    // Function to return gcd of a and b time complexity O(log(a+b))
    static int gcd(int a, int b) {
        if (a == 0) {
            return b;
        }
        return gcd(b % a, a);
    }

    //////////////////////////////////////////////////////////////////
    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 (long i = 5; i * i <= n; i = i + 6) {
            if (n % i == 0 || n % (i + 2) == 0) {
                return false;
            }
        }

        return true;
    }

    static boolean isPowerOfTwo(long n) {
        if (n == 0) {
            return false;
        }

        return (long) (Math.ceil((Math.log(n) / Math.log(2))))
                == (long) (Math.floor(((Math.log(n) / Math.log(2)))));
    }

    public static long getFact(int n) {
        long ans = 1;
        while (n > 0) {
            ans *= n;
            ans %= MOD;
            n--;
        }
        return ans;
    }

    public static long pow(long n, int pow) {
        if (pow == 0) {
            return 1;
        }
        long temp = pow(n, pow / 2) % MOD;
        temp *= temp;
        temp %= MOD;
        if (pow % 2 == 1) {
            temp *= n;
        }
        temp %= MOD;
        return temp;

    }

    public static long nCr(int n, int r) {
        long ans = 1;
        int temp = n - r;
        while (n > temp) {
            ans *= n;
            ans %= MOD;
            n--;
        }
        ans *= pow(getFact(r) % MOD, MOD - 2) % MOD;
        ans %= MOD;
        return ans;
    }

}