CF1708A Difference Operations

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 $ ?

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 $ ).

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).

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 $ .