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:
# pylint: disable=unused-variable
# pylint: enable=too-many-lines
#* Just believe in yourself


#@ Author @CAP

import os
import sys
from io import BytesIO, IOBase
import math as M
import itertools as ITR
from collections import defaultdict as D
from collections import Counter as C
from collections import deque as Q
import threading
from functools import lru_cache, reduce
from functools import cmp_to_key as CMP
from bisect import bisect_left as BL
from bisect import bisect_right as BR
import random as R
import string
import cmath,time
enum=enumerate
start_time = time.time()

#? Variables

MOD=1_00_00_00_007; MA=float("inf"); MI=float("-inf")


#? Stack increment


def increase_stack():
    sys.setrecursionlimit(2**32//2-1)
    threading.stack_size(1 << 27)
    #sys.setrecursionlimit(10**6)
    #threading.stack_size(10**8)
    t = threading.Thread(target=main)
    t.start()
    t.join()


#? Region Funtions

def prints(a):
    print(a,end=" ")

def binary(n):
    return bin(n)[2:]


def decimal(s):
    return (int(s, 2))


def pow2(n):
    p = 0
    while (n > 1):
        n //= 2
        p += 1
    return (p)

def maxfactor(n):
    q = []
    for i in range(1,int(n ** 0.5) + 1):
        if n % i == 0: q.append(i)
    if q:
        return q[-1]


def factors(n):
    q = []
    for i in range(1,int(n ** 0.5) + 1):
        if n % i == 0: q.append(i); q.append(n // i)
    return(list(sorted(list(set(q)))))

def primeFactors(n):
    l=[]
    while n % 2 == 0:
        l.append(2)
        n = n / 2
    for i in range(3, int(M.sqrt(n)) + 1, 2):
        while n % i == 0:
            l.append(i)
            n = n / i
    if n > 2:
        l.append(int(n))
    l.sort()
    return (l)


def isPrime(n):
    if (n == 1):
        return (False)
    else:
        root = int(n ** 0.5)
        root += 1
        for i in range(2, root):
            if (n % i == 0):
                return (False)
        return (True)


def seive(n):
    a = [1]
    prime = [True for i in range(n + 1)] 
    p = 2
    while (p * p <= n): 
        if (prime[p] == True): 
            for i in range(p ** 2,n + 1,p): 
                prime[i] = False
        p = p + 1
    for p in range(2,n + 1): 
        if prime[p]: 
            a.append(p)
    return(a)


def maxPrimeFactors(n):
    maxPrime = -1
    while n % 2 == 0:
        maxPrime = 2
        n >>= 1
    for i in range(3, int(M.sqrt(n)) + 1, 2):
        while n % i == 0:
            maxPrime = i
            n = n / i
    if n > 2:
        maxPrime = n
    return int(maxPrime)


def countchar(s,i):
    c=0
    ch=s[i]
    for i in range(i,len(s)):
        if(s[i]==ch):
            c+=1
        else:
            break
    return(c)

def str_counter(a):
    q = [0] * 26
    for i in range(len(a)):
        q[ord(a[i]) - 97] = q[ord(a[i]) - 97] + 1
    return(q)

def lis(arr):
    n = len(arr)
    lis = [1] * n
    maximum=0

    for i in range(1, n):
        for j in range(0, i):
            if arr[i] > arr[j] and lis[i] < lis[j] + 1:
                lis[i] = lis[j] + 1
                maximum=max(maximum,lis[i])
    return maximum


def lcm(arr):
    a=arr[0]; val=arr[0]

    for i in range(1,len(arr)):

        gcd=gcd(a,arr[i])
        a=arr[i]; val*=arr[i]

    return val//gcd

def ncr(n,r):
    return M.factorial(n) // (M.factorial(n - r) * M.factorial(r))


def npr(n,r):
    return M.factorial(n) // M.factorial(n - r)


#? Region Taking Input

def inint():
    return int(inp())

def inarr():
    return list(map(int,inp().split()))

def invar():
    return map(int,inp().split())

def instr():
    s=inp()
    return list(s)

def insarr():
    return inp().split()
#? Region Fastio

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
inp = lambda: sys.stdin.readline().rstrip("\r\n")


#<==================================== Write The Useful Code Here ============================

#< Make it one if there is some test cases
TestCases=1       #<=====================
#< =======================================
"""
> Sometimes later becomes never. Do it now.
! Be Better than yesterday.
* Your limitation—it’s only your imagination.
> Push yourself, because no one else is going to do it for you.
? The harder you work for something, the greater you’ll feel when you achieve it.
! Great things never come from comfort zones.
* Don’t stop when you’re tired. Stop when you’re done.
> Do something today that your future self will thank you for.
? It’s going to be hard, but hard does not mean impossible.
! Sometimes we’re tested not to show our weaknesses, but to discover our strengths.
"""
#@  Goal is to get Candidate Master
def solve():
    n, c = invar()
    arr = inarr()

    tot = sum(arr)
    q = c/2
    res=[]
    p = 0; j = 0
    while j < n:
        ele = arr[j] 
        if ele>c: j+=1; continue
        if q<=ele<=c:
            p=ele
            res=[j+1]; break
        if p+ele<=c:
            p+=ele
            res.append(j+1)
        j+=1
    if p<q: print(-1); return
    print(len(res))
    print(*res)


#! This is the Main Function

def main():
    flag=0
    #! Checking we are offline or not
    try:
        sys.stdin = open("c:/Users/Manoj Chowdary/Documents/python/CodeForces/contest-div-2/input.txt","r")
        sys.stdout = open("c:/Users/Manoj Chowdary/Documents/python/CodeForces/contest-div-2/output.txt","w")
    except: flag=1

    t=1
    if TestCases:
        t = inint()
    for _ in range(1,t + 1):
        solve()

    if not flag:
        print("Time: %.4f sec"%(time.time() - start_time))
        localtime = time.asctime( time.localtime(time.time()) )
        print(localtime)
        sys.stdout.close()



#? End Region


if __name__ == "__main__":

    #? Incresing Stack Limit
    #increase_stack()

    #! Calling Main Function
    main()