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:
# Author Name: Ajay Meena
# Codeforce : https://codeforces.com/profile/majay1638

# import inbuilt standard input output
import sys
import math
from sys import stdin, stdout

# //Most Frequently Used Number Theory Concepts


def sieve(N):
    primeNumbers = [True]*(N+1)
    primeNumbers[0] = False
    primeNumbers[1] = False
    i = 2
    while i*i <= N:
        j = i
        if primeNumbers[j]:
            while j*i <= N:
                primeNumbers[j*i] = False
                j += 1
        i += 1
    return primeNumbers


def getPrime(N):
    primes = sieve(N)
    result = []
    for i in range(len(primes)):
        if primes[i]:
            result.append(i)
    return result


def factor(N):
    factors = []
    i = 1
    while i*i <= N:
        if N % i == 0:
            factors.append(i)
            if i != N//i:
                factors.append(N//i)
        i += 1
    return sorted(factors)


def gcd(a, b):
    if a < b:
        return gcd(b, a)
    if b == 0:
        return a
    return gcd(b, a % b)


def extendedGcd(a, b):
    if a < b:
        return extendedGcd(b, a)
    if b == 0:
        return [a, 1, 0]
    res = extendedGcd(b, a % b)
    x = res[2]
    y = res[1]-(math.floor(a/b)*res[2])
    res[1] = x
    res[2] = y
    return res


def iterativeModularFunc(a, b, c):
    res = 1
    while b > 0:
        if b & 1:
            res = (res*a) % c
        a = (a*a) % c
        b = b//2
    return res

# // Taking Input Format Helper Function


def get_ints_in_variables():
    return map(int, sys.stdin.readline().strip().split())


def get_int(): return int(input())


def get_ints_in_list(): return list(
    map(int, sys.stdin.readline().strip().split()))


def get_list_of_list(n): return [list(
    map(int, sys.stdin.readline().strip().split())) for _ in range(n)]


def get_string(): return sys.stdin.readline().strip()


def Solution(arr, n, w):
    res = []
    s = 0
    idx = 0
    flag = 0
    for j in range(n):
        if arr[j] <= w:
            if s+arr[j] > w and 2*arr[j] < w:
                continue
            else:
                if 2*arr[j] >= w:
                    idx = j+1
                    flag = 1
                    break
                res.append(j+1)
                s += arr[j]
    if flag:
        print(1)
        print(idx)
    else:
        if len(res) > 0 and s <= w and 2*s >= w:
            print(len(res))
            for v in res:
                print(v, end=" ")
            print()
        else:
            print(-1)


def main():
    # //Write Your Code Here
    for _ in range(get_int()):
        n, w = get_ints_in_variables()
        arr = get_ints_in_list()
        Solution(arr, n, w)


#  calling main Function
if __name__ == "__main__":
    main()