Description

You are given two numbers $n, m$. You need to split $m$ into $n$ distinct positive integers (that is, the sum of these $n$ numbers is $m$), such that within the interval $[1, m]$, there is at least one positive integer that cannot be obtained by adding and subtracting these $n$ numbers (each number can be used at most once in the adding/subtracting process).

That is, let the $i$-th number among the $n$ positive integers be $a_i$. You need to ensure that within $[1, m]$, there exists at least one positive integer that cannot be represented in the form $\sum\limits^{n}_{i=1} k_i \times a_i \ (k_i \in \{-1, 0, 1\})$.

If there is no solution, output -1.

If there is a solution, output any set of $n$ positive integers that meets the requirement, and also output any number in $[1, m]$ that cannot be represented.

Input Format

This problem has multiple test cases.

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

For each test case, one line contains two positive integers $n, m$.

Output Format

For each test case:

If there is no solution, output one line -1.

If there is a solution, output $n$ positive integers in the first line, representing a valid solution, and output one positive integer in $[1, m]$ in the second line. This integer cannot be represented.

4
2 6
3 18
1 1
2 4

1 5
3
5 6 7
3
-1
-1

Hint

This problem uses bundled tests.

• Subtask 1 (10 points): $n \le 2$.
• Subtask 2 (20 points): $2n^2 \le m$.
• Subtask 3 (20 points): $\lceil 1.5n^2 \rceil \le m$.
• Subtask 4 (20 points): $n \le 5$.
• Subtask 5 (30 points): no special constraints.

Constraints: For $100\%$ of the testdata, $1 \le T \le 100$, $1 \le n, m \le 10^4$.

Translated by ChatGPT 5