CF1486A.Shifting Stacks

You have $n$ stacks of blocks. The $i$-th stack contains $h_i$ blocks and it's height is the number of blocks in it. In one move you can take a block from the $i$-th stack (if there is at least one block) and put it to the $i + 1$-th stack. Can you make the sequence of heights strictly increasing?

Note that the number of stacks always remains $n$: stacks don't disappear when they have $0$ blocks.

你有 $n$ 堆方块。第 $i$ 堆包含 $h_i$ 个方块，其高度即为其中的方块数量。在一次操作中，你可以从第 $i$ 堆（要求该堆至少有一个方块）取一个方块，并将其放到第 $i + 1$ 堆。你能否通过若干次操作使得各堆高度构成一个严格递增的序列？

注意：堆的数量始终保持为 $n$：即使某堆方块数为 $0$，该堆也不会消失。

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

The first line of each test case contains a single integer $n$ $(1 \leq n \leq 100)$. The second line of each test case contains $n$ integers $h_i$ $(0 \leq h_i \leq 10^9)$ — starting heights of the stacks.

It's guaranteed that the sum of all $n$ does not exceed $10^4$.

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

每个测试用例的第一行包含一个整数 $n$（$1 \leq n \leq 100$）。每个测试用例的第二行包含 $n$ 个整数 $h_i$（$0 \leq h_i \leq 10^9$）—— 各堆栈的初始高度。

保证所有测试用例中 $n$ 的总和不超过 $10^4$。

For each test case output YES if you can make the sequence of heights strictly increasing and NO otherwise.

You may print each letter in any case (for example, YES, Yes, yes, yEs will all be recognized as positive answer).

对于每个测试用例，如果可以使高度序列严格递增，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（例如，YES、Yes、yes、yEs 均会被识别为肯定回答）。

In the first test case there is no need to make any moves, the sequence of heights is already increasing.

In the second test case we need to move one block from the first stack to the second. Then the heights become $0$ $1$.

In the third test case we could move one block from the first stack to the second and then from the second to the third, which would make the heights $3$ $4$ $5$.

In the fourth test case we can't make a move, but the sequence is not increasing, so the answer is NO.

In the fifth test case we can only make one move (from the second to the third stack), which would make the heights $0$ $0$ $1$. Both $0$ $1$ $0$ and $0$ $0$ $1$ are not increasing sequences, so the answer is NO.

在第一个测试用例中，无需进行任何操作，高度序列本身已经是严格递增的。

在第二个测试用例中，我们需要将第一堆的一个方块移动到第二堆，此时高度变为 $0$ $1$。

在第三个测试用例中，我们可以先将第一堆的一个方块移动到第二堆，再将第二堆的一个方块移动到第三堆，从而使高度变为 $3$ $4$ $5$。

在第四个测试用例中，我们无法进行任何移动，但当前序列并非递增序列，因此答案为 NO。

在第五个测试用例中，我们只能进行一次移动（从第二堆移动到第三堆），此时高度变为 $0$ $0$ $1$。而 $0$ $1$ $0$ 和 $0$ $0$ $1$ 均不是递增序列，因此答案为 NO。