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.

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} $ ).

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.