CF1392F.Omkar and Landslide

Omkar is standing at the foot of Celeste mountain. The summit is $n$ meters away from him, and he can see all of the mountains up to the summit, so for all $1 \leq j \leq n$ he knows that the height of the mountain at the point $j$ meters away from himself is $h_j$ meters. It turns out that for all $j$ satisfying $1 \leq j \leq n - 1$, $h_j \lt h_{j + 1}$ (meaning that heights are strictly increasing).

Suddenly, a landslide occurs! While the landslide is occurring, the following occurs: every minute, if $h_j + 2 \leq h_{j + 1}$, then one square meter of dirt will slide from position $j + 1$ to position $j$, so that $h_{j + 1}$ is decreased by $1$ and $h_j$ is increased by $1$. These changes occur simultaneously, so for example, if $h_j + 2 \leq h_{j + 1}$ and $h_{j + 1} + 2 \leq h_{j + 2}$ for some $j$, then $h_j$ will be increased by $1$, $h_{j + 2}$ will be decreased by $1$, and $h_{j + 1}$ will be both increased and decreased by $1$, meaning that in effect $h_{j + 1}$ is unchanged during that minute.

The landslide ends when there is no $j$ such that $h_j + 2 \leq h_{j + 1}$. Help Omkar figure out what the values of $h_1, \dots, h_n$ will be after the landslide ends. It can be proven that under the given constraints, the landslide will always end in finitely many minutes.

Note that because of the large amount of input, it is recommended that your code uses fast IO.

奥马尔站在塞莱斯特山的山脚下。山顶距离他 $n$ 米，他能看见从当前位置一直到山顶的所有山体，因此对所有满足 $1 \leq j \leq n$ 的 $j$，他都知道距离自己 $j$ 米处的山体高度为 $h_j$ 米。事实上，对所有满足 $1 \leq j \leq n - 1$ 的 $j$，均有 $h_j \lt h_{j + 1}$（即高度严格递增）。

突然，发生了山体滑坡！在滑坡过程中，每分钟都会发生如下变化：若对某个 $j$ 满足 $h_j + 2 \leq h_{j + 1}$，则将有 $1$ 平方米的泥土从位置 $j + 1$ 滑向位置 $j$，使得 $h_{j + 1}$ 减少 $1$，同时 $h_j$ 增加 $1$。这些变化是同时发生的；例如，若对某个 $j$ 同时满足 $h_j + 2 \leq h_{j + 1}$ 和 $h_{j + 1} + 2 \leq h_{j + 2}$，那么 $h_j$ 将增加 $1$，$h_{j + 2}$ 将减少 $1$，而 $h_{j + 1}$ 则既增加 $1$ 又减少 $1$，因此该分钟内 $h_{j + 1}$ 实际保持不变。

当不存在任何 $j$ 满足 $h_j + 2 \leq h_{j + 1}$ 时，滑坡结束。请帮助奥马尔计算滑坡结束后 $h_1, \dots, h_n$ 的值。可以证明，在给定约束下，滑坡总会在有限分钟内结束。

注意：由于输入量较大，建议你的代码使用快速输入/输出（fast IO）。

The first line contains a single integer $n$ ($1 \leq n \leq 10^6$).

The second line contains $n$ integers $h_1, h_2, \dots, h_n$ satisfying $0 \leq h_1 \lt h_2 \lt \dots \lt h_n \leq 10^{12}$ — the heights.

第一行包含一个整数 $n$（$1 \leq n \leq 10^6$）。

第二行包含 $n$ 个整数 $h_1, h_2, \dots, h_n$，满足 $0 \leq h_1 \lt h_2 \lt \dots \lt h_n \leq 10^{12}$ —— 表示高度。

Output $n$ integers, where the $j$-th integer is the value of $h_j$ after the landslide has stopped.

输出 $n$ 个整数，其中第 $j$ 个整数为滑坡停止后 $h_j$ 的值。

Initially, the mountain has heights $2, 6, 7, 8$.

In the first minute, we have $2 + 2 \leq 6$, so $2$ increases to $3$ and $6$ decreases to $5$, leaving $3, 5, 7, 8$.

In the second minute, we have $3 + 2 \leq 5$ and $5 + 2 \leq 7$, so $3$ increases to $4$, $5$ is unchanged, and $7$ decreases to $6$, leaving $4, 5, 6, 8$.

In the third minute, we have $6 + 2 \leq 8$, so $6$ increases to $7$ and $8$ decreases to $7$, leaving $4, 5, 7, 7$.

In the fourth minute, we have $5 + 2 \leq 7$, so $5$ increases to $6$ and $7$ decreases to $6$, leaving $4, 6, 6, 7$.

In the fifth minute, we have $4 + 2 \leq 6$, so $4$ increases to $5$ and $6$ decreases to $5$, leaving $5, 5, 6, 7$.

In the sixth minute, nothing else can change so the landslide stops and our answer is $5, 5, 6, 7$.

最初，山的高度为 $2, 6, 7, 8$。

第一分钟，满足 $2 + 2 \leq 6$，因此 $2$ 增加至 $3$，$6$ 减少至 $5$，得到 $3, 5, 7, 8$。

第二分钟，满足 $3 + 2 \leq 5$ 和 $5 + 2 \leq 7$，因此 $3$ 增加至 $4$，$5$ 保持不变，$7$ 减少至 $6$，得到 $4, 5, 6, 8$。

第三分钟，满足 $6 + 2 \leq 8$，因此 $6$ 增加至 $7$，$8$ 减少至 $7$，得到 $4, 5, 7, 7$。

第四分钟，满足 $5 + 2 \leq 7$，因此 $5$ 增加至 $6$，$7$ 减少至 $6$，得到 $4, 6, 6, 7$。

第五分钟，满足 $4 + 2 \leq 6$，因此 $4$ 增加至 $5$，$6$ 减少至 $5$，得到 $5, 5, 6, 7$。

第六分钟，已无其他可变化的情况，滑坡停止，最终结果为 $5, 5, 6, 7$。