Background

Secret Illumination - Yooh

Problem Description

Given $n, k$, construct an array $a$ of length $n$ that satisfies the following conditions.

• $1 \le a_i \le 10^9$.
• $\displaystyle\sum_{i=1}^{n}\sum_{j=i+1}^{n}[a_i < a_j]\times a_j = k$.

Here, when the condition $case$ holds, the value of $[case]$ is $1$; otherwise it is $0$.

This problem uses Special Judge. Any answer that satisfies the conditions will be considered correct.

Input Format

This problem has multiple test cases.

The first line contains a positive integer $T$, representing the number of test cases.

The next $T$ lines each contain two integers $n, k$.

Output Format

For each test case, output one line: if there is a solution, output $n$ integers representing your constructed answer; if there is no solution, output -1.

4
4 15
7 1
3 21
10 1145141919810

2 3 1 4
-1
2009 12 21
-1

Hint

[Sample #1 Explanation]

For the first test case, we have $3+4+4+4=15$. Another valid answer is 4 2 1 5, and the value of the expression in the statement is also exactly $5+5+5=15$.

For the second test case, it is clearly impossible to construct a valid answer.

[Constraints]

This problem uses bundled tests.

For $100\%$ of the testdata, it is guaranteed that $1 \le T \le 50$, $1 \le n \le 2 \times 10^5$, and $0 \le k \le 10^{18}$.

Note: Incorrect code may cause Special Judge to exceed the time limit, in which case the result will be shown as UKE. Please be sure to take note.

Translated by ChatGPT 5