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.*;
import java.util.*;
import java.lang.*;
import java.math.*;
import java.text.DecimalFormat;
import java.lang.reflect.Array;
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.util.concurrent.Phaser;

public class A {
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
    static long MOD = (long) (1e9 + 7);
    //static int MOD = 998244353;
    static long MOD2 = MOD * MOD;
    static FastReader sc = new FastReader();
    static int pInf = Integer.MAX_VALUE;
    static int nInf = Integer.MIN_VALUE;
    public static void main(String[] args) {
        int test = 1;
        test = sc.nextInt();
        while (test-- > 0) solve();
        out.flush();
        out.close();
    }
    public static void solve() {
        int n = sc.nextInt();
        long high = sc.nextLong();
        long low = (high+1)/2;
        Pair[] a = new Pair[n];
        for(int i = 0; i < n; i++){
            int x = sc.nextInt();
            a[i] = new Pair(x,i+1);
        }
        Arrays.sort(a);
        ArrayList<Integer> ans = new ArrayList<>();
        long sum = 0L;
//        long[] pre = new long[n];
//        pre[0] = a[0].x;
//        for(int i = 1; i < n; i++){
//            pre[i] = pre[i-1]+a[i].x;
//        }
        int l = 0;
        int r = 0;
        while(l<n){
            while(r<n&&sum<=high) {
                sum += a[r].x;
                if(sum>high){
                    sum -= a[r].x;
                    break;
                }
                r++;
            }
            if(r==n&&(sum<low||sum>high)){
                out.println(-1);
                return;
            }
            if(sum>=low&&sum<=high){
                for(int i = l; i <= r-1; i++){
                    ans.add(a[i].y);
                }
                break;
            }
            //out.println(sum);
            sum -= a[l].x;
            l++;
        }
        if(ans.size()==0){
            out.println(-1);
            return;
        }
        out.println(ans.size());
        for(int g:ans){
            out.print(g+" ");
        }
        out.println();
    }
    static class Node {
        ArrayList<Node> connect = new ArrayList<>();
        int comp = -1;

        public int gsize() {
            return connect.size();
        }
    }

    static long nC2(long n) {
        return add((n * (n + 1)) / 2, 0);
    }
    public static int lowerBound(int key, int[] a) {
        int s = 0;
        int e = a.length - 1;
        if (e == -1) {
            return 0;
        }
        int ans = -1;
        while (s <= e) {
            int m = s + (e - s) / 2;
            if (a[m] >= key) {
                ans = m;
                e = m - 1;
            } else {
                s = m + 1;
            }
        }
        return ans == -1 ? s : ans;
    }

    public static int upperBound(int key, int[] a) {
        int s = 0;
        int e = a.length - 1;
        if (e == -1) {
            return 0;
        }
        int ans = -1;
        while (s <= e) {
            int m = s + (e - s) / 2;
            if (a[m] > key) {
                ans = m;
                e = m - 1;
            } else {
                s = m + 1;
            }
        }
        return ans == -1 ? s : ans;
    }

    public static long c2(long n) {
        if ((n & 1) == 0) {
            return mul(n / 2, n - 1);
        } else {
            return mul(n, (n - 1) / 2);
        }
    }

    public static long mul(long a, long b) {
        return ((a % MOD) * (b % MOD)) % MOD;
    }

    public static long add(long a, long b) {
        return ((a % MOD) + (b % MOD)) % MOD;
    }

    public static long sub(long a, long b) {
        return ((a % MOD) - (b % MOD)) % MOD;
    }

    ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//Integer.lowestOneBit(i)   Equals k where k is the position of the first one in the binary
//Integer.highestOneBit(i)  Equals k where k is the position of the last one in the binary
//Integer.bitCount(i)       returns the number of one-bits
//Collections.sort(A,(p1,p2)->(int)(p2.x-p1.x)) To sort ArrayList in descending order wrt values of x.
//            Arrays.parallelSort(a,new Comparator<TPair>() {
//      		public int compare(TPair a,TPair b) {
//        			if(a.y==b.y) return a.x-b.x;
//        			return b.y-a.y;
//        		}
//        	});
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//PrimeFactors    
    public static ArrayList<Long> primeFactors(long n) {
        ArrayList<Long> arr = new ArrayList<>();
        if (n % 2 == 0)
            arr.add((long) 2);
        while (n % 2 == 0)
            n /= 2;
        for (long i = 3; i <= Math.sqrt(n); i += 2) {
            int flag = 0;
            while (n % i == 0) {
                n /= i;
                flag = 1;
            }
            if (flag == 1)
                arr.add(i);
        }
        if (n > 2)
            arr.add(n);
        return arr;
    }

    //Pair Class
    static class Pair implements Comparable<Pair> {
        int x;
        int y;

        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }
        @Override
        public int compareTo(Pair o) {
            //out.println(this.x+" "+o.x+" "+"hi");
            if (this.x == o.x) {
                return (this.y - o.y);
            }
            return this.x-o.x;
        }
    }

    static class TPair implements Comparable<TPair> {
        int l;
        int r;
        int index;

        public TPair(int l, int r, int index) {
            this.l = l;
            this.r = r;
            this.index = index;
        }

        @Override
        public int compareTo(TPair o) {
            if (this.l == o.l) {
                return (this.r - o.r);
            }
            return (this.l - o.l);
        }
    }

    //nCr
    static long[] facts, factInvs;

    static long exp(long base, long e) {
        if (e == 0) return 1;
        long half = exp(base, e / 2);
        if (e % 2 == 0) return mul(half, half);
        return mul(half, mul(half, base));
    }

    static long modInv(long x) {
        return exp(x, MOD - 2);
    }

    static void precomp() {
        facts = new long[1_000_000];
        factInvs = new long[1_000_000];
        factInvs[0] = facts[0] = 1;
        for (int i = 1; i < facts.length; i++)
            facts[i] = mul(facts[i - 1], i);
        factInvs[facts.length - 1] = modInv(facts[facts.length - 1]);
        for (int i = facts.length - 2; i >= 0; i--)
            factInvs[i] = mul(factInvs[i + 1], i + 1);
    }

    static long nCk(int n, int k) {
        return mul(facts[n], mul(factInvs[k], factInvs[n - k]));
    }

    //Kadane's Algorithm
    static long maxSubArraySum(ArrayList<Long> a) {
        if (a.size() == 0) {
            return 0;
        }
        long max_so_far = a.get(0);
        long curr_max = a.get(0);
        for (int i = 1; i < a.size(); i++) {
            curr_max = Math.max(a.get(i), curr_max + a.get(i));
            max_so_far = Math.max(max_so_far, curr_max);
        }
        return max_so_far;
    }

    //Shuffle Sort
    static final Random random = new Random();

    static void ruffleSort(int[] a) {
        int n = a.length;//shuffle, then sort
        for (int i = 0; i < n; i++) {
            int oi = random.nextInt(n), temp = a[oi];
            a[oi] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a);
    }

    //Merge Sort
    static void merge(long arr[], int l, int m, int r) {
        // Find sizes of two subarrays to be merged
        int n1 = m - l + 1;
        int n2 = r - m;

        /* Create temp arrays */
        long L[] = new long[n1];
        long R[] = new long[n2];

        /*Copy data to temp arrays*/
        for (int i = 0; i < n1; ++i)
            L[i] = arr[l + i];
        for (int j = 0; j < n2; ++j)
            R[j] = arr[m + 1 + j];


        /* Merge the temp arrays */

        // Initial indexes of first and second subarrays
        int i = 0, j = 0;

        // Initial index of merged subarry array
        int k = l;
        while (i < n1 && j < n2) {
            if (L[i] <= R[j]) {
                arr[k] = L[i];
                i++;
            } else {
                arr[k] = R[j];
                j++;
            }
            k++;
        }

        /* Copy remaining elements of L[] if any */
        while (i < n1) {
            arr[k] = L[i];
            i++;
            k++;
        }

        /* Copy remaining elements of R[] if any */
        while (j < n2) {
            arr[k] = R[j];
            j++;
            k++;
        }
    }

    // Main function that sorts arr[l..r] using
    // merge()
    static void sort(long arr[], int l, int r) {
        if (l < r) {
            // Find the middle point
            int m = (l + r) / 2;

            // Sort first and second halves
            sort(arr, l, m);
            sort(arr, m + 1, r);

            // Merge the sorted halves
            merge(arr, l, m, r);
        }
    }

    //Brian Kernighans Algorithm
    static long countSetBits(long n) {
        if (n == 0) return 0;
        return 1 + countSetBits(n & (n - 1));
    }

    //Factorial
    static long factorial(long n) {
        if (n == 1) return 1;
        if (n == 2) return 2;
        if (n == 3) return 6;
        return n * factorial(n - 1);
    }

    //Euclidean Algorithm
    static long gcd(long A, long B) {
        if (B == 0) return A;
        return gcd(B, A % B);
    }

    //Modular Exponentiation
    static long fastExpo(long x, long n) {
        if (n == 0) return 1;
        if ((n & 1) == 0) return fastExpo((x * x) % MOD, n / 2) % MOD;
        return ((x % MOD) * fastExpo((x * x) % MOD, (n - 1) / 2)) % MOD;
    }

    //AKS Algorithm
    static boolean isPrime(long n) {
        if (n <= 1) return false;
        if (n <= 3) return true;
        if (n % 2 == 0 || n % 3 == 0) return false;
        for (int i = 5; i <= Math.sqrt(n); i += 6)
            if (n % i == 0 || n % (i + 2) == 0) return false;
        return true;
    }

    //Reverse an array
    static <T> void reverse(T arr[], int l, int r) {
        Collections.reverse(Arrays.asList(arr).subList(l, r));
    }

    //Print array
    static void print1d(long arr[]) {
        out.println(Arrays.toString(arr));
    }

    static void print2d(int arr[][]) {
        for (int a[] : arr) out.println(Arrays.toString(a));
    }

    //Sieve of eratosthenes
    static int[] findPrimes(int n) {
        boolean isPrime[] = new boolean[n + 1];
        ArrayList<Integer> a = new ArrayList<>();
        int result[];
        Arrays.fill(isPrime, true);
        isPrime[0] = false;
        isPrime[1] = false;
        for (int i = 2; i * i <= n; ++i) {
            if (isPrime[i] == true) {
                for (int j = i * i; j <= n; j += i) isPrime[j] = false;
            }
        }
        for (int i = 0; i <= n; i++) if (isPrime[i] == true) a.add(i);
        result = new int[a.size()];
        for (int i = 0; i < a.size(); i++) result[i] = a.get(i);
        return result;

    }

    //Indivisual factors of all nos till n
    static ArrayList<Integer>[] indiFactors(int n) {
        ArrayList<Integer>[] A = new ArrayList[n + 1];
        for (int i = 0; i <= n; i++) {
            A[i] = new ArrayList<>();
        }
        int[] sieve = new int[n + 1];
        for (int i = 2; i <= n; i++) {
            if (sieve[i] == 0) {
                for (int j = i; j <= n; j += i)
                    if (sieve[j] == 0) {
                        //sieve[j]=i;
                        A[j].add(i);
                    }
            }
        }
        return A;
    }

    //Segmented Sieve
    static boolean[] segmentedSieve(long l, long r) {
        boolean[] segSieve = new boolean[(int) (r - l + 1)];
        Arrays.fill(segSieve, true);
        int[] prePrimes = findPrimes((int) Math.sqrt(r));
        for (int p : prePrimes) {
            long low = (l / p) * p;
            if (low < l) {
                low += p;
            }
            if (low == p) {
                low += p;
            }
            for (long j = low; j <= r; j += p) {
                segSieve[(int) (j - l)] = false;
            }
        }
        if (l == 1) {
            segSieve[0] = false;
        }
        return segSieve;
    }

    //Euler Totent function
    static long countCoprimes(long n) {
        ArrayList<Long> prime_factors = new ArrayList<>();
        long x = n, flag = 0;
        while (x % 2 == 0) {
            if (flag == 0) prime_factors.add(2L);
            flag = 1;
            x /= 2;
        }
        for (long i = 3; i * i <= x; i += 2) {
            flag = 0;
            while (x % i == 0) {
                if (flag == 0) prime_factors.add(i);
                flag = 1;
                x /= i;
            }
        }
        if (x > 2) prime_factors.add(x);
        double ans = (double) n;
        for (Long p : prime_factors) {
            ans *= (1.0 - (Double) 1.0 / p);
        }
        return (long) ans;
    }

    static long modulo = (long) 1e9 + 7;

    public static long modinv(long x) {
        return modpow(x, modulo - 2);
    }

    public static long modpow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        long x = modpow(a, b / 2);
        x = (x * x) % modulo;
        if (b % 2 == 1) {
            return (x * a) % modulo;
        }
        return x;
    }

    public static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        //it reads the data about the specified point and divide the data about it ,it is quite fast
        //than using direct

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception r) {
                    r.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());//converts string to integer
        }

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (Exception r) {
                r.printStackTrace();
            }
            return str;
        }
    }
}