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 PYTHON3):

Solution:
from collections import Counter
import string
import math
import sys
# sys.setrecursionlimit(10**6) 
from fractions import Fraction
def array_int():
    return [int(i) for i in sys.stdin.readline().split()]
def vary(arrber_of_variables):
    if arrber_of_variables==1:
        return int(sys.stdin.readline())
    if arrber_of_variables>=2:
        return map(int,sys.stdin.readline().split()) 
def makedict(var):
    return dict(Counter(var))
# i am noob wanted to be better and trying hard for that
def printDivisors(n): 
    divisors=[]  
    # Note that this loop runs till square root 
    i = 1
    while i <= math.sqrt(n): 
          
        if (n % i == 0) : 
              
            # If divisors are equal, print only one 
            if (n//i == i) : 
                divisors.append(i) 
            else : 
                # Otherwise print both 
                divisors.extend((i,n//i)) 
        i = i + 1
    return divisors
def countTotalBits(num):
     binary = bin(num)[2:]
     return(len(binary))
def isPrime(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 or n % 3 == 0) : 
        return False
  
    i = 5
    while(i * i <= n) : 
        if (n % i == 0 or n % (i + 2) == 0) : 
            return False
        i = i + 6
  
    return True
mod=10**9+7
# def ncr(n,r):
#     if n<r:
#         return 0
#     if n==r:
#         return 1
#     numer=fact[n]
#     # print(numer)
#     denm=(fact[n-r]*fact[r])
#     # print(denm)
#     return numer*pow(denm,mod-2,mod)
# def dfs(node):
#     global graph,m,cats,count,visited,val
#     # print(val)
#     visited[node]=1
#     if cats[node]==1:
#         val+=1
    
    
#     # print(val)
#     for i in graph[node]:
#         if visited[i]==0:
#             z=dfs(i)
#             # print(z,i)
#             count+=z
#     if val>m:
#         val-=1
#         return 0
#     else:
#         return 1
    
    
# fact=[1]*(1001)
# c=1
# mod=10**9+7
# for i in range(1,1001):
#     fact[i]=(fact[i-1]*i)%mod
# print(fact)
def comp(x):
    return x[1]
def SieveOfEratosthenes(n): 
    global primes
    # Create a boolean array "prime[0..n]" and initialize 
    #  all entries it as true. A value in prime[i] will 
    # finally be false if i is Not a prime, else true. 
    prime = [True for i in range(n+1)] 
    p = 2
    while (p * p <= n): 
          
        # If prime[p] is not changed, then it is a prime 
        if (prime[p] == True): 
              
            # Update all multiples of p 
            for i in range(p * p, n+1, p): 
                prime[i] = False
        p += 1
      
    # Print all prime numbers 
    for p in range(2, n+1): 
        if prime[p]: 
            primes.append(p*p)
primes=[]
# SieveOfEratosthenes(2*(10**6))
def binary_search(arr, x):
    low = 0
    high = len(arr) - 1
    mid = 0
    while low <= high:
        mid = (high + low) // 2
  
        # Check if x is present at mid 
        if arr[mid] < x: 
            low = mid + 1
  
        # If x is greater, ignore left half 
        elif arr[mid] > x: 
            high = mid - 1
  
        # If x is smaller, ignore right half 
        else: 
            return mid 
  
    # If we reach here, then the element was not present 
    return -1
testCases=1
testCases=vary(1)
for _ in range(testCases):
    n,w=vary(2)
    num=array_int()
    
    if 1:
        pum=[]
        for i in range(n):
            pum.append([num[i],i+1])
        pum.sort(reverse=True)
        sumt=0
        ans=[]
        for i in range(n):
            if sumt+pum[i][0]>(w):
                continue
            else:
                sumt+=pum[i][0]
                ans.append(pum[i][1])
                if sumt>=(w/2):
                    break                
        if sumt>=(w/2):
            print(len(ans))
            print(*ans)
        else:
            print(-1)