CF1823A A-characteristic

Consider an array $ a_1, a_2, \dots, a_n $ consisting of numbers $ 1 $ and $ -1 $ . Define $ A $ -characteristic of this array as a number of pairs of indices $ 1 \le i < j \le n $ , such that $ a_i \cdot a_j = 1 $ . Find any array $ a $ with given length $ n $ with $ A $ -characteristic equal to the given value $ k $ .

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 100 $ ). The description of the test cases follows. The only line of each test case contains two integers $ n $ and $ k $ ( $ 2 \le n \le 100 $ ; $ 0 \le k \le \frac{(n-1) n}{2} $ ) — the length of required array and required $ A $ -characteristic.

For each test case, if there is no array $ a $ with given $ A $ -characteristic $ k $ , print NO. Otherwise, print YES and $ n $ numbers $ 1 $ and $ -1 $ , which form the required array $ a $ . If there are multiple answers, print any of them.

In the first test case, there is only one pair of different elements in the array, and their product is $ a_1 \cdot a_2 = -1 \neq 1 $ , hence its $ A $ -characteristic is $ 0 $ . In the second test case, there is only one pair of different elements in the array, and their product is $ a_1 \cdot a_2 = 1 $ , hence its $ A $ -characteristic is $ 1 $ . In the third test case, there are three pairs of different elements in the array, and their product are: $ a_1 \cdot a_2 = -1 $ , $ a_1 \cdot a_3 = 1 $ , $ a_2 \cdot a_3 = -1 $ , hence its $ A $ -characteristic is $ 1 $ . In the fourth test case, we can show, that there is no array with length $ 3 $ , which $ A $ -characteristic is $ 2 $ .