CF1809C.Sum on Subarrays

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.

对于数组 $a = [a_1, a_2, \dots, a_n]$，我们用 $a[l, r]$ 表示其子数组 $[a_l, a_{l+1}, \dots, a_r]$。

例如，数组 $a = [1, -3, 1]$ 共有 $6$ 个非空子数组：

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

给定两个整数 $n$ 和 $k$，请构造一个由 $n$ 个整数组成的数组 $a$，使得：

• $a$ 中所有元素均在 $-1000$ 到 $1000$ 之间；
• $a$ 恰好有 $k$ 个子数组的和为正；
• 其余 $\dfrac{(n+1) \cdot n}{2}-k$ 个子数组的和为负。

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 $k$ ($2 \le n \le 30$; $0 \le k \le \dfrac{(n+1) \cdot n}{2}$).

第一行包含一个整数 $t$（$1 \le t \le 5000$）—— 测试用例的数量。

每个测试用例由一行组成，包含两个整数 $n$ 和 $k$（$2 \le n \le 30$；$0 \le k \le \dfrac{(n+1) \cdot n}{2}$）。

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.

对于每个测试用例，输出 $n$ 个整数——即满足约束条件的数组元素。可以证明答案一定存在。若存在多个答案，输出任意一个即可。