CF1848C.Vika and Price Tags

Vika came to her favorite cosmetics store "Golden Pear". She noticed that the prices of $n$ items have changed since her last visit.

She decided to analyze how much the prices have changed and calculated the difference between the old and new prices for each of the $n$ items.

Vika enjoyed calculating the price differences and decided to continue this process.

Let the old prices be represented as an array of non-negative integers $a$, and the new prices as an array of non-negative integers $b$. Both arrays have the same length $n$.

In one operation, Vika constructs a new array $c$ according to the following principle: $c_i = |a_i - b_i|$. Then, array $c$ renamed into array $b$, and array $b$ renamed into array $a$ at the same time, after which Vika repeats the operation with them.

For example, if $a = [1, 2, 3, 4, 5, 6, 7]$; $b = [7, 6, 5, 4, 3, 2, 1]$, then $c = [6, 4, 2, 0, 2, 4, 6]$. Then, $a = [7, 6, 5, 4, 3, 2, 1]$; $b = [6, 4, 2, 0, 2, 4, 6]$.

Vika decided to call a pair of arrays $a$, $b$ dull if after some number of such operations all elements of array $a$ become zeros.

Output "YES" if the original pair of arrays is dull, and "NO" otherwise.

维卡来到了她最喜欢的化妆品店“金梨”。她注意到，自上次光顾以来，店内 $n$ 种商品的价格发生了变化。

她决定分析价格变化幅度，并计算了每种商品新旧价格之间的差值。

维卡很享受计算这些价格差的过程，于是决定将这一操作持续进行下去。

设旧价格表示为一个非负整数数组 $a$，新价格表示为一个非负整数数组 $b$。两个数组长度均为 $n$。

在一次操作中，维卡按如下规则构造一个新数组 $c$：$c_i = |a_i - b_i|$。接着，将数组 $c$ 重命名为数组 $b$，同时将原数组 $b$ 重命名为数组 $a$，然后用更新后的 $a$ 和 $b$ 重复该操作。

例如，若 $a = [1, 2, 3, 4, 5, 6, 7]$，$b = [7, 6, 5, 4, 3, 2, 1]$，则 $c = [6, 4, 2, 0, 2, 4, 6]$；随后 $a = [7, 6, 5, 4, 3, 2, 1]$，$b = [6, 4, 2, 0, 2, 4, 6]$。

维卡将一对数组 $a$、$b$ 称为“乏味的”（dull），如果经过若干次上述操作后，数组 $a$ 的所有元素均变为 $0$。

若初始数组对是“乏味的”，输出 "YES"；否则输出 "NO"。

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

The first line of each test case contains a single integer $n$ ($1 \le n \le 10^5$) — the number of items whose prices have changed.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le 10^9$) — the old prices of the items.

The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ($0 \le b_i \le 10^9$) — the new prices of the items.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \le t \le 10^4$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 10^5$），表示价格发生变化的商品数量。

第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$0 \le a_i \le 10^9$），表示商品的原价。

第三行包含 $n$ 个整数 $b_1, b_2, \ldots, b_n$（$0 \le b_i \le 10^9$），表示商品的新价。

保证所有测试用例的 $n$ 之和不超过 $10^5$。

For each test case, output "YES" if the pair of price arrays is dull, and "NO" otherwise.

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

对于每个测试用例，如果价格数组对是“单调的”（dull），则输出 “YES”，否则输出 “NO”。

你可以以任意大小写形式输出每个字母（小写或大写）。例如，字符串 “yEs”、“yes”、“Yes” 和 “YES” 均可被接受为肯定回答。

In the first test case, the array $a$ is initially zero.

In the second test case, after the first operation $a = [1, 2, 3], b = [0, 0, 0]$. After the second operation $a = [0, 0, 0], b = [1, 2, 3]$.

In the third test case, it can be shown that the array $a$ will never become zero.

在第一个测试用例中，数组 $a$ 初始时全为零。

在第二个测试用例中，第一次操作后 $a = [1, 2, 3], b = [0, 0, 0]$；第二次操作后 $a = [0, 0, 0], b = [1, 2, 3]$。

在第三个测试用例中，可以证明数组 $a$ 永远不会变为全零。