CF1931B.Make Equal

There are $n$ containers of water lined up, numbered from left to right from $1$ to $n$. Each container can hold any amount of water; initially, the $i$-th container contains $a_i$ units of water. The sum of $a_i$ is divisible by $n$.

You can apply the following operation any (possibly zero) number of times: pour any amount of water from the $i$-th container to the $j$-th container, where $i$ must be less than $j$ (i.e. $i \lt j$). Any index can be chosen as $i$ or $j$ any number of times.

Determine whether it is possible to make the amount of water in all containers the same using this operation.

有 $n$ 个装有水的容器从左到右排成一列，编号为 $1$ 到 $n$。每个容器可容纳任意量的水；初始时，第 $i$ 个容器中含有 $a_i$ 单位的水。所有 $a_i$ 的总和能被 $n$ 整除。

你可以执行以下操作任意次（包括零次）：从第 $i$ 个容器向第 $j$ 个容器倾倒任意数量的水，其中 $i$ 必须小于 $j$（即 $i \lt j$）。任意下标均可多次作为 $i$ 或 $j$ 被选择。

判断是否能通过该操作使所有容器中的水量相等。

The first line of the input contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Then the descriptions of the test cases follow.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of containers with water.

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 10^9$) — the amounts of water in the containers. It is guaranteed that the sum of $a_i$ in each test case does not exceed $2 \cdot 10^9$. Also, the sum of $a_i$ is divisible by $n$.

It is guaranteed that the sum of $n$ over all test cases in the input does not exceed $2 \cdot 10^5$.

输入的第一行包含一个整数 $t$（$1 \le t \le 10^4$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^5$），表示装有水的容器数量。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$0 \le a_i \le 10^9$），表示各容器中的水量。保证每个测试用例中所有 $a_i$ 的总和不超过 $2 \cdot 10^9$，且该总和能被 $n$ 整除。

保证输入中所有测试用例的 $n$ 值之和不超过 $2 \cdot 10^5$。

Output $t$ lines, each of which is the answer to the corresponding test case. As the answer, output "YES" if it is possible to make the amount of water in all containers the same using the described operation. Otherwise, output "NO".

You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

输出 $t$ 行，每行对应一个测试用例的答案。若能通过上述操作使所有容器中的水量相等，则输出 "YES"；否则输出 "NO"。

每个字母可为任意大小写（小写或大写）。例如，字符串 "yEs"、"yes"、"Yes" 和 "YES" 均被视为正确答案。

In the third test case of the example ($a=[4, 5, 2, 1, 3]$), you can proceed as follows:

• pour $1$ unit of water from the first vessel to the fourth, then $a=[3, 5, 2, 2, 3]$;
• pour $1$ unit of water from the second vessel to the third, then $a=[3, 4, 3, 2, 3]$;
• pour $1$ unit of water from the second vessel to the fourth, then $a=[3, 3, 3, 3, 3]$.

在示例的第三个测试用例中（$a=[4, 5, 2, 1, 3]$），你可以按如下方式操作：

• 将第一个容器中的 $1$ 单位水倒入第四个容器，此时 $a=[3, 5, 2, 2, 3]$；
• 将第二个容器中的 $1$ 单位水倒入第三个容器，此时 $a=[3, 4, 3, 2, 3]$；
• 将第二个容器中的 $1$ 单位水倒入第四个容器，此时 $a=[3, 3, 3, 3, 3]$。