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 Main {
    static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 
    
    public static void sort(int arr[],int l,int r) {    //sort(arr,0,n-1);
        if(l==r) {
            return;
        }
        int mid=(l+r)/2;
        sort(arr,l,mid);
        sort(arr,mid+1,r);
        merge(arr,l,mid,mid+1,r);
    }
    public static void merge(int arr[],int l1,int r1,int l2,int r2) {
        int tmp[]=new int[r2-l1+1];
        int indx1=l1,indx2=l2;
        //sorting the two halves using a tmp array
        for(int i=0;i<tmp.length;i++) {
            if(indx1>r1) {
                tmp[i]=arr[indx2];
                indx2++;
                continue;
            }
            if(indx2>r2) {
                tmp[i]=arr[indx1];
                indx1++;
                continue;
            }
            if(arr[indx1]<arr[indx2]) {
                tmp[i]=arr[indx1];
                indx1++;
                continue;
            }
            tmp[i]=arr[indx2];
            indx2++;
        }
        //Copying the elements of tmp into the main array
        for(int i=0,j=l1;i<tmp.length;i++,j++) {
            arr[j]=tmp[i];
        }
    }
    
    public static void sort(long arr[],int l,int r) {    //sort(arr,0,n-1);
        if(l==r) {
            return;
        }
        int mid=(l+r)/2;
        sort(arr,l,mid);
        sort(arr,mid+1,r);
        merge(arr,l,mid,mid+1,r);
    }
    public static void merge(long arr[],int l1,int r1,int l2,int r2) {
        long tmp[]=new long[r2-l1+1];
        int indx1=l1,indx2=l2;
        //sorting the two halves using a tmp array
        for(int i=0;i<tmp.length;i++) {
            if(indx1>r1) {
                tmp[i]=arr[indx2];
                indx2++;
                continue;
            }
            if(indx2>r2) {
                tmp[i]=arr[indx1];
                indx1++;
                continue;
            }
            if(arr[indx1]<arr[indx2]) {
                tmp[i]=arr[indx1];
                indx1++;
                continue;
            }
            tmp[i]=arr[indx2];
            indx2++;
        }
        //Copying the elements of tmp into the main array
        for(int i=0,j=l1;i<tmp.length;i++,j++) {
            arr[j]=tmp[i];
        }
    }
    
    public static void main(String args[]) throws IOException {
        Reader input=new Reader();
        StringBuilder ans=new StringBuilder("");
        int test=input.nextInt();
        for(int tt=1;tt<=test;tt++) {
            int n=input.nextInt();
            long wei=input.nextLong();
            int arr[]=new int[n];
            for(int i=0;i<n;i++) {
                arr[i]=input.nextInt();
            }
            ans.append(solve(n,wei,arr));
        }
        System.out.println(ans);
    }
    public static StringBuilder solve(int n,long w,int arr[]) {
        long lim=(w/2)+(w%2);
        for(int i=0;i<n;i++) {
            if(arr[i]>=lim && arr[i]<=w) {
                return new StringBuilder("1\n"+(i+1)+"\n");
            }
        }
        int indx[]=new int[n];
        for(int i=0;i<n;i++) {
            indx[i]=i;
        }
        sort(arr,indx,n);
        int cnt=0;
        boolean taken[]=new boolean[n];
        long total=0;
        for(int i=0;i<n;i++) {
            if(total+arr[i]>w) {
                break;
            }
            cnt++;
            total+=arr[i];
            taken[indx[i]]=true;
        }
        if(total<lim) {
            return new StringBuilder("-1\n");
        }
        StringBuilder ans=new StringBuilder("");
        ans.append(cnt+"\n");
        for(int i=0;i<n;i++) {
            if(taken[i]) {
                ans.append((i+1)+" ");
            }
        }
        ans.append("\n");
        return ans;
    }
    
    
    static void buildMaxHeap(int arr[],int brr[], int n) 
  { 
    for (int i = 1; i < n; i++) 
    { 
      // if child is bigger than parent 
      if (arr[i] > arr[(i - 1) / 2]) 
      { 
        int j = i; 
  
        // swap child and parent until 
        // parent is smaller 
        while (arr[j] > arr[(j - 1) / 2]) 
        { 
          swap(arr, j, (j - 1) / 2); 
          swap(brr, j, (j - 1) / 2); 
          j = (j - 1) / 2; 
        } 
      } 
    } 
  } 
  
  static void sort(int arr[],int brr[], int n) 
  { 
    buildMaxHeap(arr,brr, n); 
  
    for (int i = n - 1; i > 0; i--) 
    { 
      // swap value of first indexed 
      // with last indexed 
      swap(arr, 0, i); 
      swap(brr, 0, i); 
  
      // maintaining heap property 
      // after each swapping 
      int j = 0, index; 
  
      do
      { 
        index = (2 * j + 1); 
  
        // if left child is smaller than 
        // right child point index variable 
        // to right child 
        if (index < (i - 1) && arr[index] < arr[index + 1]) 
          index++; 
  
        // if parent is smaller than child 
        // then swapping parent with child 
        // having higher value 
        if (index < i && arr[j] < arr[index]) {
          swap(arr, j, index); 
          swap(brr, j, index);
        }
  
        j = index; 
  
      } while (index < i); 
    } 
  } 
  
  public static void swap(int[] a, int i, int j) { 
    int temp = a[i]; 
    a[i]=a[j]; 
    a[j] = temp; 
  } 
}