A. A-characteristictime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputConsider 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.InputEach 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.OutputFor 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.ExampleInput
72 02 13 13 23 35 45 5Output
YES
1 -1 
YES
1 1 
YES
1 -1 1 
NO
YES
1 1 1 
YES
-1 1 -1 1 1 
NONoteIn 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.
72 02 13 13 23 35 45 5
YES 1 -1  YES 1 1  YES 1 -1 1  NO YES 1 1 1  YES -1 1 -1 1 1  NO
['combinatorics', 'constructive algorithms', 'math', '*800']