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.*;
import java.io.*;
public class Solution {
    static Scanner in =new Scanner(System.in);
    static final Random random=new Random();
    //static int mod=1000_000_007;
    public static void main(String[] args) {
      int tt=in.nextInt();in.nextLine();
       outer: while(tt-->0){
           int n=in.nextInt();long W=in.nextLong();
           int w[][]=readAr(n);
           long l=(W+1)/2;
           Arrays.sort(w,(a,b)->a[0]-b[0]);
           if(w[0][0]>W){
               System.out.println(-1);continue outer;
           }
           for(int x[]:w){
               if(x[0]>=l && x[0]<=W){System.out.println(1);System.out.println(x[1]);continue outer;}
           }
           int i=0;
           for( i=1;i<n;i++){
               if(w[i][0]>W)break;
               //w[i][0]+=w[i-1][0];
           }
           long sum=0;
           for(int k=0,j=0;j<i;j++){
               //System.out.print(sum);
               sum+=w[j][0];
               if(sum>=l && sum<=W){
                   System.out.println(j-k+1);
                   for(int k1=k;k1<=j;k1++)System.out.print(w[k1][1]+" ");
                   System.out.println();
                   continue outer;
               }
               if(sum>W)sum-=w[k--][0];
           }
           System.out.println(-1);
       }    
    }
    static int nCr(int n, int r,int p){
        if (r == 0) return 1; 
        if(r==1)return n;
        return ((int)fact(n)*modInverse((int)fact(r),p)%p * modInverse((int)fact(n-r),p) % p)%p; 
    }
    static int modInverse(int n, int p) { 
        return power(n, p - 2, p); 
    } 
    static int power(int x, int y, int p) { 
        int res = 1;
        x = x % p;
        while (y > 0) {
            if (y % 2 == 1) 
                res = (res * x) % p;
            y = y >> 1;
            x = (x * x) % p; 
        }
        return res; 
    } 
    static int find(int p){
        int m=0;int l=0,r=p;
        while(l<=r){
            int mid=l+(r-l)/2;
            if(mid!=r)m++;
            if(mid==r)break;
            if(mid<r)l=mid+1;
        }return m;
    }
    static int[][] readAr(int n) {
        int[][] a=new int[n][2];
        for (int i=0; i<n; i++) {a[i][0]=in.nextInt();a[i][1]=i+1;}
        return a;
	}
    static int fact(int k){
        long[]f=new long[10001];f[1]=1;
        for(int i=2;i<10001;i++){
            f[i]=(i*f[i-1]%1000000007);
        }
        return (int)f[k];
    }
	static void ruffleSort(int[] a) {
		int n=a.length;
		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);
	}
	static void reverse(int []a){
        int n= a.length;
        for(int i=0;i<n/2;i++){
        int temp=a[i];
        a[i]=a[n-i-1];
        a[n-i-1]=temp;
        a[i]=-a[i];
        }
        debug(a);
	}
	static void debug(int []a) {
        for (int i=0; i<a.length;i++) System.out.print(a[i]+" ");
	}
	static void print(List<Integer>s) {
        for(int x:s) System.out.print(x+",");
        System.out.println();
	}
	static int gcd(int a, int b) {
        return b==0 ? a : gcd(b, a % b);
	}
    static int find_max(int []a){
        int m=Integer.MIN_VALUE;
        for(int x:a)m=Math.max(x,m);
        return m;
    }
    static int find_min(int []a){
        int m=Integer.MAX_VALUE;
        for(int x:a)m=Math.min(x,m);
        return m;
    }
}