A-characteristic

Description:

Input:

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.

Output:

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.

Sample Input:

7
2 0
2 1
3 1
3 2
3 3
5 4
5 5

Sample Output:

YES
1 -1 
YES
1 1 
YES
1 -1 1 
NO
YES
1 1 1 
YES
-1 1 -1 1 1 
NO

Note:

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 $$$2$$$.