codeforces#P1708A. Difference Operations
Difference Operations
Description
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).
Input
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 $a_1,a_2,\ldots,a_n$ ($1 \le a_i \le 10^9$).
Output
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).
Samples
4
2
5 10
3
1 2 3
4
1 1 1 1
9
9 9 8 2 4 4 3 5 3
YES
YES
YES
NO
Note
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 $4$, $3$, $2$.