Playing with GCD

题意翻译

给定有 $n$ 个整数的数列 $a$，求是否可以构造出一个有 $n+1$ 个数的数列 $b$，使得对于任意的 $i$，都有 $a_i=\gcd(b_i,b_{i+1})$，可以则输出 `YES`，否则输出 `NO`。

题目描述

You are given an integer array $ a $ of length $ n $ . Does there exist an array $ b $ consisting of $ n+1 $ positive integers such that $ a_i=\gcd (b_i,b_{i+1}) $ for all $ i $ ( $ 1 \leq i \leq n $ )? Note that $ \gcd(x, y) $ denotes the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers $ x $ and $ y $ .

输入输出格式

输入格式

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \leq t \leq 10^5 $ ). Description of the test cases follows. The first line of each test case contains an integer $ n $ ( $ 1 \leq n \leq 10^5 $ ) — the length of the array $ a $ . The second line of each test case contains $ n $ space-separated integers $ a_1,a_2,\ldots,a_n $ representing the array $ a $ ( $ 1 \leq a_i \leq 10^4 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^5 $ .

输出格式

For each test case, output "YES" if such $ b $ exists, otherwise output "NO". You can print each letter in any case (upper or lower).

输入输出样例

输入样例 #1

4
1
343
2
4 2
3
4 2 4
4
1 1 1 1

输出样例 #1

YES
YES
NO
YES

说明

In the first test case, we can take $ b=[343,343] $ . In the second test case, one possibility for $ b $ is $ b=[12,8,6] $ . In the third test case, it can be proved that there does not exist any array $ b $ that fulfills all the conditions.

题意翻译

给定有 $n$ 个整数的数列 $a$，求是否可以构造出一个有 $n+1$ 个数的数列 $b$，使得对于任意的 $i$，都有 $a_i=\gcd(b_i,b_{i+1})$，可以则输出 `YES`，否则输出 `NO`。