C. Sum on Subarrays
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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

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

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.

Example
Input
4
3 2
2 0
2 2
4 6
Output
1 -3 1
-13 -42
-13 42
-3 -4 10 -2