A15927. 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 $2$ .