Difference Operations
题意翻译
给你 $n$ 个数 $a_1,a_2,\ldots,a_n$,每次可以的进行如下操作 :
- 选择 $i(2 \leq i \leq n)$,让 $a_i \gets a_i - a_{i - 1}$
问能否进行若干次操作后,使得 $a_i = 0 (2 \leq i \leq n )$。
题目描述
You are given an array $ a $ consisting of $ n $ positive integers.
You are allowed to perform this operation any number of times (possibly, zero):
- choose an index $ i $ ( $ 2 \le i \le n $ ), and change $ a_i $ to $ a_i - a_{i-1} $ .
Is it possible to make $ a_i=0 $ for all $ 2\le i\le n $ ?
输入输出格式
输入格式
The input consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1\le t\le 100 $ ) — the number of test cases. The description of the test cases follows.
The first line contains one integer $ n $ ( $ 2 \le n \le 100 $ ) — the length of array $ a $ .
The second line contains $ n $ integers $ a_1,a_2,\ldots,a_n $ ( $ 1 \le a_i \le 10^9 $ ).
输出格式
For each test case, print "YES" (without quotes), if it is possible to change $ a_i $ to $ 0 $ for all $ 2 \le i \le n $ , and "NO" (without quotes) otherwise.
You can print letters in any case (upper or lower).
输入输出样例
输入样例 #1
4
2
5 10
3
1 2 3
4
1 1 1 1
9
9 9 8 2 4 4 3 5 3
输出样例 #1
YES
YES
YES
NO
说明
In the first test case, the initial array is $ [5,10] $ . You can perform $ 2 $ operations to reach the goal:
1. Choose $ i=2 $ , and the array becomes $ [5,5] $ .
2. Choose $ i=2 $ , and the array becomes $ [5,0] $ .
In the second test case, the initial array is $ [1,2,3] $ . You can perform $ 4 $ operations to reach the goal:
1. Choose $ i=3 $ , and the array becomes $ [1,2,1] $ .
2. Choose $ i=2 $ , and the array becomes $ [1,1,1] $ .
3. Choose $ i=3 $ , and the array becomes $ [1,1,0] $ .
4. Choose $ i=2 $ , and the array becomes $ [1,0,0] $ .
In the third test case, you can choose indices in the order $ 4 $ , $ 3 $ , $ 2 $ .