G. GCD vs. LCM
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Faris loves to play with numbers. Today, he's looking for an interesting array. He defines an array of $$$n$$$ positive integers to be interesting if it satisfies the following property: $$$$$$\gcd(a_1, a_2, \dots, a_n) \lt \gcd(a_1, \dots, a_{i - 1}, a_{i + 1}, \dots, a_n) \text{ for all integer } i \text{ where } 1 \le i \le n$$$$$$

In other words, the GCD of the entire array is strictly less than the GCD of any subset formed by removing exactly one element.

Being amazed by this property, Faris has challenged you, a famous mathematician, to construct any such interesting array of size $$$n$$$ — but with an extra challenge: the LCM of the elements of the array cannot exceed $$$l$$$.

Given two integers $$$n$$$ and $$$l$$$, your task is to construct such an array, or report that it is impossible.

The greatest common divisor or GCD of a set of positive integers is the largest positive integer that divides all of them. Formally, $$$$$$\gcd(a_1, a_2, \dots, a_n) = \max \Bigl\{ d \in \mathbb{Z}^+ \ \big|\ d \mid a_i \ \forall i \in \{1, 2, \dots, n\} \Bigr\} $$$$$$

The least common multiple or LCM of a set of positive integers is the smallest positive integer that is divisible by all of them. Formally, $$$$$$\mathrm{lcm}(a_1, a_2, \dots, a_n) = \min \Bigl\{ m \in \mathbb{Z}^+ \ \big|\ a_i \mid m \ \forall i \in \{1, 2, \dots, n\} \Bigr\}$$$$$$

Input

The first line of the input contains a single integer $$$t \: (1 \leq t \leq 10^5)$$$ — the number of test cases. Then $$$t$$$ test cases follow.

Each test case consists of a single line containing two space-separated integers $$$n \: (2 \leq n \le 10^5)$$$ and $$$l \: (1 \leq l \le 10^{18})$$$ — the size of the array to be constructed and the maximum allowed LCM.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \times 10^5$$$.

Output

For each test case, output $$$n$$$ space-separated positive integers — the elements of the interesting array.

If no such array exists, output $$$-1$$$.

Example
Input
2
3 500
4 200
Output
21 60 70
-1
Note

For the first test case, $$$\gcd(21, 60, 70) = 1$$$ and $$$\mathrm{lcm}(21, 60, 70) = 420 \lt 500$$$. Here, $$$1 \lt \gcd(21, 60) = 3$$$, $$$1 \lt \gcd(21, 70) = 7$$$ and $$$1 \lt \gcd(60, 70) = 10$$$.

For the second test case, it can be proven that no interesting array exists under the given constraints.