310369: CF1823A. A-characteristic
Description
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 $k$.
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.
ExampleInput7 2 0 2 1 3 1 3 2 3 3 5 4 5 5Output
YES 1 -1 YES 1 1 YES 1 -1 1 NO YES 1 1 1 YES -1 1 -1 1 1 NONote
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 $2$.
Input
题意翻译
构建一个长度为 $n$ 的数组，数组元素只能为 $1$ 或者 $-1$。 定义数组每满足一对 $a_{i} \cdot a_{j} = 1$ $( 1 \leq i < j \leq n )$ 为有 $1$ 个特征 $A$。求数组是否能构成出满足刚好 $k$ 个特征 $A$。如果能构成该数组输出 YES 并给出构造数组。反之只输出 NO。Output
输入数据格式：第一行包含一个整数t(1 ≤ t ≤ 100)，表示测试用例的数量。接下来t行，每行包含两个整数n和k(2 ≤ n ≤ 100; 0 ≤ k ≤ (n-1)n/2)，分别表示数组的长度和A特性值。
输出数据格式：对于每个测试用例，如果不存在满足条件的数组a，输出"NO"。否则，输出"YES"和一个由n个1和-1组成的数组a。如果有多个答案，输出其中任意一个。题目大意：给定一个由1和-1组成的数组a，定义A特性为满足a_i * a_j = 1的索引对(i, j)的数量。给定数组长度n和A特性值k，构造一个满足条件的数组a。 输入数据格式：第一行包含一个整数t(1 ≤ t ≤ 100)，表示测试用例的数量。接下来t行，每行包含两个整数n和k(2 ≤ n ≤ 100; 0 ≤ k ≤ (n-1)n/2)，分别表示数组的长度和A特性值。 输出数据格式：对于每个测试用例，如果不存在满足条件的数组a，输出"NO"。否则，输出"YES"和一个由n个1和-1组成的数组a。如果有多个答案，输出其中任意一个。