1809C · Sum on Subarrays

Problem: For an array $a = [a_1, a_2, \dots, a_n]$, let's denote its subarray $a[l, r]$ as the array $[a_l, a_{l+1}, \dots, a_r]$.

For example, the array $a = [1, -3, 1]$ has $6$ non-empty subarrays:

• $a[1,1] = [1]$;
• $a[1,2] = [1,-3]$;
• $a[1,3] = [1,-3,1]$;
• $a[2,2] = [-3]$;
• $a[2,3] = [-3,1]$;
• $a[3,3] = [1]$.

You are given two integers $n$ and $k$. Construct an array $a$ consisting of $n$ integers such that:

• all elements of $a$ are from $-1000$ to $1000$;
• $a$ has exactly $k$ subarrays with positive sums;
• the rest $\dfrac{(n+1) \cdot n}{2}-k$ subarrays of $a$ have negative sums.

Input Format: The first line contains one integer $t$ ($1 \le t \le 5000$) — the number of test cases.

Each test case consists of one line containing two integers $n$ and $k$ ($2 \le n \le 30$; $0 \le k \le \dfrac{(n+1) \cdot n}{2}$).

Output Format: For each test case, print $n$ integers — the elements of the array meeting the constraints. It can be shown that the answer always exists. If there are multiple answers, print any of them.