CF2244B.Nikita and Books

As is well known, Nikita loves reading. Today, he made a mess in his room and arranged his books into $n$ stacks in a row, numbered from $1$ to $n$ from left to right. The $i$-th stack contains $a_i$ books. This arrangement is called neat if, in every stack except the rightmost one, the number of books is strictly less than in the stack to its right; that is, the array $a$ is strictly increasing.

Yura wants to make the arrangement neat by performing the following operation any number of times:

1. Choose a stack $i$ such that $1 \le i \lt n$ and $a_i \gt 1$.
2. Take $1$ book from the top of stack $i$, so $a_i$ decreases by $1$.
3. Put this book on top of stack $i + 1$, so $a_{i+1}$ increases by $1$.

Determine whether Yura can make the arrangement neat.

众所周知，尼基塔非常喜欢阅读。今天，他把房间弄得一团糟，将他的书排成了从左到右编号为 $1$ 到 $n$ 的 $n$ 堆。第 $i$ 堆包含 $a_i$ 本书。若除最右边一堆外，每一堆的书本数量都严格小于其右边一堆的数量（即数组 $a$ 是严格递增的），则称该排列是“整齐的”。

尤拉希望通过执行以下操作任意多次，使该排列变得整齐：

1. 选择一个满足 $1 \le i \lt n$ 且 $a_i \gt 1$ 的堆 $i$；
2. 从堆 $i$ 的顶部取走 $1$ 本书，使得 $a_i$ 减少 $1$；
3. 将这本书放在堆 $i + 1$ 的顶部，使得 $a_{i+1}$ 增加 $1$。

请判断尤拉是否能使该排列变得整齐。

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

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

The second line of each test case contains $n$ integers $a_i$ ($1 \le a_i \le 10^9$) — the initial number of books in each stack.

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

第一行包含一个整数 $t$（$1 \le t \le 10^4$）——测试用例的数量。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^5$）——堆栈的数量。

每个测试用例的第二行包含 $n$ 个整数 $a_i$（$1 \le a_i \le 10^9$）——每堆初始的书本数量。

保证所有测试用例的 $n$ 之和不超过 $2 \cdot 10^5$。

For each test case, output "YES" if Yura can make the arrangement neat, and "NO" otherwise.

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

对于每个测试用例，如果尤拉能使排列变得整齐，则输出 “YES”，否则输出 “NO”。

您可以以任意大小写形式输出每个字母（小写或大写）。例如，字符串 “yEs”、“yes”、“Yes” 和 “YES” 均可被接受。

null