【Gym - 101350 D - Magical Bamboos 】& gcd

In a magical forest, there exists N bamboos that don’t quite get cut down the way you would expect.

Originally, the height of the ith bamboo is equal to hi. In one move, you can push down a bamboo and decrease its height by one, but this move magically causes all the other bamboos to increase in height by one.

If you can do as many moves as you like, is it possible to make all the bamboos have the same height?

Input

The first line of input is T – the number of test cases.

The first line of each test case contains an integer N (1 ≤ N ≤ 105) - the number of bamboos.

The second line contains N space-separated integers hi (1 ≤ hi ≤ 105) - the original heights of the bamboos.

Output

For each test case, output on a single line “yes” (without quotes), if you can make all the bamboos have the same height, and “no” otherwise.

Example

Input

2

3

2 4 2

2

1 2

Output

yes

no

题意 ： 给出 n 个人要吃的食物量，问选者什么型号的盘子（型号 o 的盘子可以盛的食物的量为 o），每个人盛的食物的量恰好等于每个要吃的食物的量,满足条件的情况下 o 尽可能的大

思路 ： gcd，因为 1 的时满足条件

AC代码：

#include<cstdio>
#include<cmath>
#include<map>
#include<cstring>
#include<algorithm>
using namespace std;
const int MAX = 1e5 + 10;
typedef long long LL;
int gcd(int a,int b){ return a % b == 0 ? b : gcd(b,a % b); }
int main()
{
int T; scanf("%d",&T);
while(T--){
int n,a,o = -1; scanf("%d",&n);
LL ans = 0;
for(int i = 0 ; i< n; i++){
scanf("%d",&a);
o = o == -1 ? a : gcd(a,o);
ans += a;
}
printf("%lld %d\n",ans,o);
}
return 0;
}