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.math.BigInteger;
											import java.sql.Array;
										    import java.util.ArrayList;
											import java.util.Arrays;
											import java.util.Collection;
											import java.util.Collections;
											import java.util.Comparator;
											import java.util.HashMap;
											import java.util.InputMismatchException;
											import java.util.Iterator;
											import java.util.LinkedHashSet;
											import java.util.LinkedList;
											import java.util.List;
											import java.util.Map;
											import java.util.Map.Entry;	
											import java.util.PriorityQueue;
											import java.util.Queue;
											import java.util.Scanner;
											import java.util.Set;
											import java.util.Stack;
											import java.io.BufferedReader;
											import java.io.IOException;
											import java.io.InputStream;
											import java.io.InputStreamReader;
											import java.util.Scanner;
											import java.util.StringTokenizer;
											import java.util.TreeMap;
											import java.util.TreeSet;
											
											
											
											public class Main {
												
											static long l[];	
											static int k;	
													
												static InputReader rd=new InputReader(System.in);
											
												public static void main(String[] args) {
													Scanner sc=new Scanner(System.in);
													
													int t=sc.nextInt();
													outer:while(t-->0) {
														
														long n=sc.nextLong();
														long W=sc.nextLong();
														ArrayList<Long> A=new ArrayList<>();
														for(int i=0;i<n;i++) {
															
															A.add(sc.nextLong());
														}
														
														long tot=0;
														
														ArrayList<Integer> ans=new ArrayList<>();
														for(int i=0;i<n;i++) {
															if(A.get(i)>=(W+1)/2&&A.get(i)<=W) {
																System.out.println(1);
																System.out.println(i+1);
																continue outer;
															}
															
															if(tot+A.get(i)<=W&&tot+A.get(i)>0&&A.get(i)<=W)
															{
																
															tot+=A.get(i);
															ans.add(i+1);
															
															}
															
															
														}
														
														//System.out.println(tot);
														if(ans.size()==0||tot<(W+1)/2) {
															System.out.println(-1);
															continue;
														}
														
														System.out.println(ans.size());
														
															for(int i=0;i<ans.size();i++) {
															
														System.out.print(ans.get(i)+" ");
														}
														
														System.out.println();
														
														
											}
													
													}
															
															
												public static int removeDuplicateElementsFromArray(int array[], int arrayLength){
											        //Checking the length of the passed array
											        if (arrayLength==0 || arrayLength==1){
											            return arrayLength;
											        }
											        //Creating a temporary array of the passed array lenght
											        int[] temp = new int[arrayLength];
											        int j = 0;
											        //For Loop itteration
											        for (int i=0; i<arrayLength-1; i++){
											            if (array[i] != array[i+1]){
											                temp[j++] = array[i];
											            }
											         }
											        //Setting the last element of array to the temp
											        temp[j++] = array[arrayLength-1];
											        // Changing original array
											        for (int i=0; i<j; i++){
											            array[i] = temp[i];
											        }
											        return j;
											    }	
														
														
													static class Naruto{
														
														int a;int i;
														
														public Naruto(int a ,int i) {
															// TODO Auto-generated constructor stub
														this.a=a;
														this.i=i;
														}
														
													}
													
													
													
													
											
													
												static long power1(long x, long y, long p) 
											    { 
											        // Initialize result 
											        long res = 1;      
											         
											        // Update x if it is more   
											        // than or equal to p 
											        x = x % p;  
											  
											       if (x == 0) return 0; // In case x is divisible by p;    
											  
											        while (y > 0) 
											        { 
											            // If y is odd, multiply x 
											            // with result 
											            if((y & 1)==1) 
											                res = (res * x) % p; 
											      
											            // y must be even now 
											            // y = y / 2 
											            y = y >> 1;  
											            x = (x * x) % p;  
											        } 
											        return res; 
											    } 	
									static void dfs(ArrayList<ArrayList<graph>> g,int v,boolean visited[]) {
										
										visited[v]=true;
										l[k]+=1;
										for(graph j:g.get(v)) {
											if(j.c==0) {
												//System.out.println(v);
												if(!visited[j.v])
												dfs(g,j.v,visited);  
											}
											
										}
										
										
									}
												
												
									static class graph{
										int v;int c;
										public graph(int v,int c) {
											// TODO Auto-generated constructor stub
											this.v=v;
											this.c=c;
										
										}
										
									}
												
												
													
												
										static		long fact(long n) {
													
													if(n<=1)return 1;
													else return n*fact(n-1);
												}
												
								 static long maxCrossingSum(long arr[], int l, 
							                                int m, int h) 
							    { 
							        // Include elements on left of mid. 
							       long sum = 0; 
							        long left_sum = Integer.MIN_VALUE; 
							        for (int i = m; i >= l; i--) 
							        { 
							            sum = sum + arr[i]; 
							            if (sum > left_sum) 
							            left_sum = sum; 
							        } 
							  
							        // Include elements on right of mid 
							        sum = 0; 
							        long right_sum = Integer.MIN_VALUE; 
							        for (int i = m + 1; i <= h; i++) 
							        { 
							            sum = sum + arr[i]; 
							            if (sum > right_sum) 
							            right_sum = sum; 
							        } 
							  
							        // Return sum of elements on left 
							        // and right of mid 
							       // returning only left_sum + right_sum will fail for [-2, 1] 
							        return Math.max(left_sum + right_sum, Math.max(left_sum, right_sum)); 
							    } 
							  
							    // Returns sum of maxium sum subarray  
							    // in aa[l..h] 
							    static long maxSubArraySum(long arr[], int l,  
							                                      int h) 
							    { 
							    // Base Case: Only one element 
							    if (l == h) 
							        return arr[l]; 
							  
							    // Find middle point 
							    int m = (l + h)/2; 
							  
							    /* Return maximum of following three  
							    possible cases: 
							    a) Maximum subarray sum in left half 
							    b) Maximum subarray sum in right half 
							    c) Maximum subarray sum such that the  
							    subarray crosses the midpoint */
							    return Math.max(Math.max(maxSubArraySum(arr, l, m), 
							                    maxSubArraySum(arr, m+1, h)), 
							                    maxCrossingSum(arr, l, m, h)); 
							    } 
												
												static long abs(long a) {
													return Math.abs(a);
												}
												
												static class seg{
													
													int x;int y;int l;
													public seg(int x,int y,int l) {
														this.x=x;
														this.y=y;
														this.l=l;
														// TODO Auto-generated constructor stub
													}
													
													
												}
											static	boolean isPresent(int j,int p) {
													
													int i=(j/50)%475;
													
													for(int k=0;k<25;k++) {
													    i = (i * 96 + 42)% 475;
													    if(26+i==p)return true;
														}
													return false;
													
												}
																				
												static class Helper{
													int val;int index;
													public Helper(int  val,int index) {
														
														this.val=val;
														this.index=index;
														// TODO Auto-generated constructor stub
													}
												}
											
										
												
								
											    static boolean isPrime(int 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 (int i = 5; i * i <= n; i = i + 6) 
											            if (n % i == 0 || n % (i + 2) == 0) 
											                return false; 
											  
											        return true; 
											    } 
										
												      
												    /* Iterative Function to calculate 
												       (x^y)%p in O(log y) */
												    static long power(long x, long y, long p) 
												    { 
												        // Initialize result 
												        long res = 1;      
												         
												        // Update x if it is more   
												        // than or equal to p 
												        x = x % p;  
												  
												       if (x == 0) return 0; // In case x is divisible by p;    
												  
												        while (y > 0) 
												        { 
												            // If y is odd, multiply x 
												            // with result 
												            if((y & 1)==1) 
												                res = (res * x) % p; 
												      
												            // y must be even now 
												            // y = y / 2 
												            y = y >> 1;  
												            x = (x * x) % p;  
												        } 
												        return res; 
												    } 
									
												
												
												
												  static class InputReader {
												        private InputStream stream;
												        private byte[] buf = new byte[1024];
												        private int curChar;
												        private int numChars;
												        private SpaceCharFilter filter;
											
												        public InputReader(InputStream stream) {
												            this.stream = stream;
												        }
											
												        public int read() {
												            if (numChars == -1)
												                throw new InputMismatchException();
												            if (curChar >= numChars) {
												                curChar = 0;
												                try {
												                    numChars = stream.read(buf);
												                } catch (IOException e) {
												                    throw new InputMismatchException();
												                }
												                if (numChars <= 0)
												                    return -1;
												            }
												            return buf[curChar++];
												        }
											
												        public int readInt() {
												            int c = read();
												            while (isSpaceChar(c))
												                c = read();
												            int sgn = 1;
												            if (c == '-') {
											    sgn = -1;
											    c = read();
											}
											int res = 0;
											do {
											    if (c < '0' || c > '9')
											        throw new InputMismatchException();
											    res *= 10;
											    res += c - '0';
											        c = read();
											    } while (!isSpaceChar(c));
											    return res * sgn;
											}
											
											public String readString() {
											    int c = read();
											    while (isSpaceChar(c))
											        c = read();
											    StringBuilder res = new StringBuilder();
											    do {
											        res.appendCodePoint(c);
											        c = read();
											    } while (!isSpaceChar(c));
											    return res.toString();
											}
											
											public boolean isSpaceChar(int c) {
											    if (filter != null)
											        return filter.isSpaceChar(c);
											    return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
												        }
											
												        public String next() {
												            return readString();
												        }
											
												    }
												
												  public interface SpaceCharFilter {
												        public boolean isSpaceChar(int ch);
												    }	
												
												
																					
																					
																					
																		
											}