CF1708A.Difference Operations

普及/提高-

通过率：0%

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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#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#1

YES
YES
YES
NO

说明/提示

In the first test case, the initial array is $[5,10]$ . You can perform $2$ operations to reach the goal:

Choose $i=2$ , and the array becomes $[5,5]$ .
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:

Choose $i=3$ , and the array becomes $[1,2,1]$ .
Choose $i=2$ , and the array becomes $[1,1,1]$ .
Choose $i=3$ , and the array becomes $[1,1,0]$ .
Choose $i=2$ , and the array becomes $[1,0,0]$ .

In the third test case, you can choose indices in the order $4$ , $3$ , $2$ .

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