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:
# DEFINING SOME GOOD STUFF
from math import *
import threading
import sys
mod = 10**9 + 7
 
# _______________________________________________________________#
 
def npr(n,r):
	return factorial(n)//factorial(n-r) if n >= r else 0
 
 
def lower_bound(li, num):
	answer = -1
	start = 0
	end = len(li) - 1
 
	while (start <= end):
		middle = (end + start) // 2
		if li[middle] >= num:
			answer = middle
			end = middle - 1
		else:
			start = middle + 1
	return answer  # index where x is not less than num
 
 
def upper_bound(li, num):
	answer = -1
	start = 0
	end = len(li) - 1
 
	while (start <= end):
		middle = (end + start) // 2
 
		if li[middle] <= num:
			answer = middle
			start = middle + 1
 
		else:
			end = middle - 1
	return answer  # index where x is not greater than num
 
 
def abs(x):
	return x if x >= 0 else -x
 
 
def binary_search(li, val, lb, ub):
	ans = -1
	while (lb <= ub):
		mid = (lb + ub) // 2
		# print(mid, li[mid])
		if li[mid] > val:
			ub = mid - 1
		elif val > li[mid]:	
			lb = mid + 1
		else:
			ans = mid # return index
			break
	return ans
 
 
def kadane(x):  # maximum sum contiguous subarray
	sum_so_far = 0
	current_sum = 0
	for i in x:
		current_sum += i
		if current_sum < 0:
			current_sum = 0
		else:
			sum_so_far = max(sum_so_far, current_sum)
	return sum_so_far
 
 
def pref(li):
	pref_sum = [0]
	for i in li:
		pref_sum.append(pref_sum[-1] + i)
	return pref_sum
 
 
def graph(n, m):
	adj = dict()
	for i in range(1, n + 1):
		adj.setdefault(i, 0)
	for i in range(m):
		a, b = map(int, input().split())
		adj[a] += 1
		adj[b] += 1
	return adj
 
 
def SieveOfEratosthenes(n):
	prime = [True for i in range(n+1)]
	p = 2
	li = []
	while (p * p <= n):
		if (prime[p] == True):
			for i in range(p * p, n+1, p):
				prime[i] = False
		p += 1
 
	for p in range(2, len(prime)):
		if prime[p]:
			li.append(p)
	return li
 
def primefactors(n):
	factors = []
	while(n%2 == 0):
		factors.append(2)
		n //= 2
	for i in range(3, int(sqrt(n))+1, 2): #only odd factors left
		while n%i == 0:
			factors.append(i)
			n //= i
	if n>2: # incase of prime
		factors.append(n)
	return factors
 
def prod(li):
	ans = 1
	for i in li:
		ans *= i
	return ans
# _______________________________________________________________#
 
 
 
sys.setrecursionlimit(300000)
# threading.stack_size(10**5)  # remember it cause mle
#def main():
for _ in range(int(input()) if True else 1):
	#n = int(input())
	n,w = map(int, input().split())
	#s = list(input())
	#s = [int(x) for x in s]
	a = list(map(int, input().split()))
	#b = list(map(int,input().split()))
	#s = input()
	#c = list(map(int,input().split()))
	# adj = graph(n,m)
	b = []
	for i in range(n):
		b.append((a[i], i+1))
	b.sort()
	weight = 0
	ans = []
	f = 0
	for i in range(n):
		weight += b[i][0]
		
		ans.append(b[i][1])
		if weight > w:
			if b[i][0] >= (w+1)//2 and b[i][0] <= w:
				ans = [b[i][1]]
				f = 1
			break
		elif weight >= (w+1)//2:
			f = 1
			break
	ans.sort()
	if f:
		print(len(ans))
		print(*ans)
	else:
		print(-1)

	

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
	
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
'''		
t = threading.Thread(target=main)
t.start()
t.join()
'''