A15185. 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 $4$ , $3$ , $2$ .