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 defaultdict,OrderedDict,Counter
from sys import stdin,stdout
from bisect import bisect_left,bisect_right
# import numpy as np
from queue import Queue,PriorityQueue
from heapq import heapify,heappop,heappush
from statistics import median
from math import gcd,sqrt,floor,factorial,ceil,log2,log10
import fractions
import copy
from copy import deepcopy
import sys
sys.setrecursionlimit(10**7)
import math
import os
import bisect
import collections
mod=pow(10,9)+7
import random
from random import random,randint,randrange
def ncr(n, r, p=mod):
    num = den = 1
    for i in range(r):
        num = (num * (n - i)) % p
        den = (den * (i + 1)) % p
    return (num * pow(den,
            p - 2, p)) % p
# input=stdin.readline
# print=stdout.write
inf=float("inf")
adj=defaultdict(set)
visited=defaultdict(int)
def addedge(a,b):
    adj[a].add(b)
    adj[b].add(a)
def bfs(v):
    q=Queue()
    q.put(v)
    visited[v]=1
    while q.qsize()>0:
        s=q.get_nowait()
        print(s)
        for i in adj[s]:
            if visited[i]==0:
                q.put(i)
                visited[i]=1
def dfs(v,visited):
    if visited[v]==1:
        return;
    visited[v]=1

    print(v)
    for i in adj[v]:
        dfs(i,visited)
# a9=pow(10,6)+10
# prime = [True for i in range(a9 + 1)]
# def SieveOfEratosthenes(n):
#     p = 2
#     while (p * p <= n):
#         if (prime[p] == True):
#             for i in range(p * p, n + 1, p):
#                 prime[i] = False
#         p += 1
def reverse_bisect_right(a, x, lo=0, hi=None):
    if lo < 0:
        raise ValueError('lo must be non-negative')
    if hi is None:
        hi = len(a)
    while lo < hi:
        mid = (lo+hi)//2
        if x > a[mid]:
            hi = mid
        else:
            lo = mid+1
    return lo
def reverse_bisect_left(a, x, lo=0, hi=None):
    if lo < 0:
        raise ValueError('lo must be non-negative')
    if hi is None:
        hi = len(a)
    while lo < hi:
        mid = (lo+hi)//2
        if x >= a[mid]:
            hi = mid
        else:
            lo = mid+1
    return lo


class MaxHeap:

    def __init__(self, maxsize):

        self.maxsize = maxsize
        self.size = 0
        self.Heap = [0] * (self.maxsize + 1)
        self.Heap[0] = sys.maxsize
        self.FRONT = 1

    def parent(self, pos):

        return pos // 2

    def leftChild(self, pos):

        return 2 * pos

    def rightChild(self, pos):

        return (2 * pos) + 1

    def isLeaf(self, pos):

        if pos >= (self.size // 2) and pos <= self.size:
            return True
        return False

    def swap(self, fpos, spos):

        self.Heap[fpos], self.Heap[spos] = (self.Heap[spos],
                                            self.Heap[fpos])

    def maxHeapify(self, pos):

        if not self.isLeaf(pos):
            if (self.Heap[pos] < self.Heap[self.leftChild(pos)] or
                    self.Heap[pos] < self.Heap[self.rightChild(pos)]):

                if (self.Heap[self.leftChild(pos)] >
                        self.Heap[self.rightChild(pos)]):
                    self.swap(pos, self.leftChild(pos))
                    self.maxHeapify(self.leftChild(pos))

                else:
                    self.swap(pos, self.rightChild(pos))
                    self.maxHeapify(self.rightChild(pos))


    def insert(self, element):

        if self.size >= self.maxsize:
            return
        self.size += 1
        self.Heap[self.size] = element

        current = self.size

        while (self.Heap[current] >
               self.Heap[self.parent(current)]):
            self.swap(current, self.parent(current))
            current = self.parent(current)
    def Print(self):

        for i in range(1, (self.size // 2) + 1):
            print(" PARENT : " + str(self.Heap[i]) +
                  " LEFT CHILD : " + str(self.Heap[2 * i]) +
                  " RIGHT CHILD : " + str(self.Heap[2 * i + 1]))
    def extractMax(self):

        popped = self.Heap[self.FRONT]
        self.Heap[self.FRONT] = self.Heap[self.size]
        self.size -= 1
        self.maxHeapify(self.FRONT)

        return popped

def get_list():
    return list(map(int,input().split()))
def get_str_list_in_int():
    return [int(i) for i in list(input())]
def get_str_list():
    return list(input())
def get_map():
    return map(int,input().split())
def input_int():
    return int(input())
def matrix(a,b):
    return [[0 for i in range(b)] for j in range(a)]
def swap(a,b):
    return b,a
def find_gcd(l):
    a=l[0]
    for i in range(len(l)):
        a=gcd(a,l[i])
    return a;
def is_prime(n):
    sqrta=int(sqrt(n))
    for i in range(2,sqrta+1):
        if n%i==0:
            return 0;
    return 1;
def prime_factors(n):
    sqrta = int(sqrt(n))
    for i in range(2,sqrta+1):
        if n%i==0:
            return [i]+prime_factors(n//i)
    return [n]
def fun(n,k):
    return n//k*(k-1)
def kth_no(n,k):
    # index=1;
    # count=n%k;
    # k_pow=k;
    # while n>k_pow:
    #     k_pow = pow(k, index)
    #     index+=1
    #     count+=fun(n,k_pow)
    # return count
    return n // k * (k - 1) + n % k

nc="NO"
yc="YES"
ns="No"
ys="Yes"
# t=1;
t=input_int()
for i in range(t):
    n,W=get_map();
    w=get_list()
    dict=defaultdict(list)
    for i in range(n):
        dict[w[i]].append(i+1)
    lower=ceil(W/2)
    upper=W
    found=0
    for i in range(n):
        if lower<=w[i]<=upper:
            print(1)
            print(i+1)
            found=1;
            break;
    if found:
        continue
    if sum(w)<lower:
        print(-1)
        continue
    if min(w)>upper:
        print(-1)
        continue
    wt=[i for i in w if i<=upper]
    if sum(wt)<lower:
        print(-1)
        continue
    else:
        res=[]
        wt.sort()
        suma=0;
        index=0
        while not lower<=suma<=upper and index<len(wt):
            suma+=wt[index]
            res.append(wt[index])
            index+=1

        print(len(res))
        for i in res:
            print(dict[i].pop(),end=" ")
    print("")