CF1805C.Place for a Selfie

The universe is a coordinate plane. There are $n$ space highways, each of which is a straight line $y=kx$ passing through the origin $(0, 0)$. Also, there are $m$ asteroid belts on the plane, which we represent as open upwards parabolas, i. e. graphs of functions $y=ax^2+bx+c$, where $a \gt 0$.

You want to photograph each parabola. To do this, for each parabola you need to choose a line that does not intersect this parabola and does not touch it. You can select the same line for different parabolas. Please find such a line for each parabola, or determine that there is no such line.

宇宙是一个坐标平面。平面上有 $n$ 条太空高速公路，每条都是一条过原点 $(0, 0)$ 的直线 $y=kx$。此外，平面上还有 $m$ 条小行星带，我们将其表示为开口向上的抛物线，即函数 $y=ax^2+bx+c$ 的图像，其中 $a \gt 0$。

你需要为每条抛物线拍摄一张照片。为此，对每条抛物线，你都需要选择一条既不与该抛物线相交、也不与该抛物线相切的直线。不同抛物线可以选用同一条直线。请为每条抛物线找出这样的一条直线，或判定不存在这样的直线。

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

The first line of each test case contains $2$ integers $n$ and $m$ ($1 \le n, m \le 10^5$) —the number of lines and parabolas, respectively.

Each of the next $n$ lines contains one integer $k$ ($|k| \le 10^8$), denoting a line that is described with the equation $y=kx$. The lines are not necessarily distinct, $k$ can be equal to $0$.

Each of the next $m$ lines contains $3$ integers $a$, $b$, and $c$ ($a, |b|, |c| \le 10^8$, $a \gt 0$) — coefficients of equations of the parabolas $ax^2+bx+c$. The parabolas are not necessarily distinct.

It is guaranteed that the sum $n$ over all test cases does not exceed $10^5$, and the sum $m$ over all test cases also does not exceed $10^5$.

每个测试包含多个测试用例。第一行包含测试用例数量 $t$（$1 \le t \le 10^4$）。随后是各测试用例的描述。

每个测试用例的第一行包含两个整数 $n$ 和 $m$（$1 \le n, m \le 10^5$），分别表示直线的数量和抛物线的数量。

接下来的 $n$ 行中，每行包含一个整数 $k$（$|k| \le 10^8$），表示一条由方程 $y=kx$ 描述的直线。这些直线不一定互不相同，且 $k$ 可以为 $0$。

再接下来的 $m$ 行中，每行包含三个整数 $a$、$b$ 和 $c$（$a, |b|, |c| \le 10^8$，且 $a \gt 0$），表示抛物线 $ax^2+bx+c$ 的系数。这些抛物线不一定互不相同。

保证所有测试用例中 $n$ 的总和不超过 $10^5$，且所有测试用例中 $m$ 的总和也不超过 $10^5$。

For each test case, output the answers for each parabola in the given order. If there is a line that does not intersect the given parabola and doesn't touch it, print on a separate line the word "YES", and then on a separate line the number $k$ — the coefficient of this line. If there are several answers, print any of them. If the line does not exist, print one word "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

The empty lines in the output in the example are given only for illustration, you do not need to output them (but you can).

对于每个测试用例，按给定顺序输出每条抛物线对应的答案。如果存在一条直线既不与给定抛物线相交，也不与之相切，则在单独一行输出单词 “YES”，然后在下一行输出该直线的系数 $k$。若存在多个满足条件的答案，输出任意一个即可。若这样的直线不存在，则仅输出单词 “NO”。

你可以以任意大小写形式输出答案（大写或小写均可）。例如，字符串 “yEs”、“yes”、“Yes” 和 “YES” 均会被识别为肯定回答。

示例输出中的空行仅为示意之用，你无需输出它们（但也可以输出）。

In the first test case, both parabolas do not intersect the only given line $y=1\cdot x$, so the answer is two numbers $1$.

In the second test case, the line $y=x$ and the parabola $2x^2+5x+1$ intersect, and also the line $y=4x$ and the parabola $x^2+2x+1$ touch, so these pairs do not satisfy the condition. So for the first parabola, the answer is $1$ ($y=1x$), and for the second parabola — $4$.

In the third test set, the line and the parabola intersect, so the answer is "NO".

在第一个测试用例中，两条抛物线均不与给定的唯一直线 $y=1\cdot x$ 相交，因此答案是两个数字 $1$。

在第二个测试用例中，直线 $y=x$ 与抛物线 $2x^2+5x+1$ 相交，且直线 $y=4x$ 与抛物线 $x^2+2x+1$ 相切，因此这两对均不满足条件。故对于第一条抛物线，答案为 $1$（即直线 $y=1x$），而对于第二条抛物线，答案为 $4$。

在第三个测试用例中，直线与抛物线相交，因此答案为 “NO”。