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.util.*;
public class Main{

    static Scanner sc = new Scanner(System.in);
    static int mod = 1_000_000_007;
    public static void main(String[] args){
        int t = sc.nextInt();
        for (int i = 0; i < t; i++) {
            solve();
        }
    }
    private static void solve(){
        int len = sc.nextInt();
        long w = sc.nextLong();
        Integer[] arr = new Integer[len];
        Integer[]p = new Integer[len];
        for (int i = 0; i < len; i++) {
            arr[i] = sc.nextInt();
            p[i] = i;
        }
        Arrays.sort(p, new Comparator<Integer>() {
            @Override
            public int compare(Integer o1, Integer o2) {
                return arr[o2] - arr[o1];
            }
        });
        long cur = 0;
        ArrayList<Integer>ans = new ArrayList<>();
        boolean find = false;
        for (int i = 0;i < len;i++){
            if(cur + arr[p[i]] <= w){
                cur += arr[p[i]];
                ans.add(p[i] + 1);
            }
            if(cur >= (w + 1)/2){
                find =true;
                break;
            }
        }
        if(find){
            System.out.println(ans.size());
            printList(ans);
        } else{
            System.out.println(-1); 
        }
    }
    // 3
    // 2 2 3 4
    private static void solve2() {
        find = false;
        if(ans != null)
        ans.clear();
        int len = sc.nextInt();
        long w = sc.nextLong();
        int[] arr = readArr(len);
        LinkedList<Integer> con = new LinkedList<>();
        dfs(arr,con,0,0l,w);
        if(find){
            System.out.println(ans.size());
            printList(ans);
        } else{
            System.out.println(-1);
        }
    }
    private static boolean find = false;
    static ArrayList<Integer>ans;
    private static void dfs(int[]arr,LinkedList<Integer>con,int cur,long sum,long w){
        if(find || cur == arr.length)
            return;
        dfs(arr,con,cur + 1,sum,w);
        sum += arr[cur];
        con.addLast(cur + 1);
        if(sum <= w){
            if(sum >= (w + 1)/2){
                find = true;
                ans = new ArrayList<>(con);
                return;
            }else{
                dfs(arr,con,cur + 1,sum,w);
            }
        }
        con.removeLast();
    }

    private static ArrayList<ArrayList<Integer>>g(int n){
        ArrayList<ArrayList<Integer>> g = new ArrayList<>();
        for (int i = 0; i < (n + 1); i++) {
            g.add(new ArrayList<>());
        }
        for (int i = 0; i < n - 1; i++) {
            int u = sc.nextInt();
            int v = sc.nextInt();
            g.get(u).add(v);
            g.get(v).add(u);
        }
        return g;
    }
    private static int gcb(int a,int b){
        if(a == b)
            return a;
        if(a < b)
            return gcb(b,a);
        if(a % b == 0)
            return b;
        return gcb(b,a % b);
    }

    private static void printList(List<Integer> arr){
        for(int i : arr){
            System.out.print(i + " ");
        }
        System.out.println();
    }
    private static void printArr(int[]arr){
        for(int i : arr){
            System.out.print(i + " ");
        }
        System.out.println();
    }
    private static int[]readArr(int len){
        int[]ans = new int[len];
        for(int i = 0;i < len;i++){
            ans[i] = sc.nextInt();
        }
        return ans;
    }
    private static long powmod(long a,long b){
        long res=1;
        for(long i=0;i<b;i++){
            res=res*a%mod;
        }
        return res;
    }
}