CF1184E3.Daleks' Invasion (hard)

With your help, Heidi has prepared a plan of trap placement and defence. Yet suddenly, the Doctor popped out of the TARDIS and told her that he had spied on the Daleks' preparations, and there is more of them than ever. Desperate times require desperate measures, so Heidi is going to risk meeting with the Daleks and she will consider placing a trap along any Corridor.

This means she needs your help again in calculating $E_{max}(c)$ – the largest $e \le 10^9$ such that if we changed the energy requirement of $c$ to $e$, then the Daleks might use $c$ in their invasion – but this time for all Time Corridors.

在你的帮助下，海蒂已经制定了一套陷阱布置与防御计划。然而，博士突然从TARDIS中现身，告诉她：他已侦察到戴立克的备战情况，而此次戴立克的数量比以往任何时候都更多。危急时刻需要采取非常手段，因此海蒂决定冒险与戴立克正面接触，并考虑在**任意时间走廊（Time Corridor）**上布置陷阱。

这意味着她再次需要你的帮助，来计算 $E_{max}(c)$ —— 即最大的 $e \le 10^9$，使得若将走廊 $c$ 的能量需求修改为 $e$，则戴立克可能在入侵过程中使用该走廊 $c$；但这一次，需对所有时间走廊均进行此计算。

First line: number $n$ of destinations, number $m$ of corridors ($2 \leq n \leq 10^5$, $n - 1 \leq m \leq 10^6$). The next $m$ lines: destinations $a$, $b$ and energy $e$ ($1 \leq a, b \leq n$, $a \neq b$, $0 \leq e \leq 10^9$).

No pair ${a, b}$ will repeat. The graph is guaranteed to be connected. It is not guaranteed that all energy requirements $e$ are distinct, or that the minimum spanning tree is unique.

第一行：目的地数量 $n$，走廊数量 $m$（$2 \leq n \leq 10^5$，$n - 1 \leq m \leq 10^6$）。接下来的 $m$ 行：目的地 $a$、$b$ 及所需能量 $e$（$1 \leq a, b \leq n$，$a \neq b$，$0 \leq e \leq 10^9$）。

任意一对 $\{a, b\}$ 不会重复出现。图保证连通。不保证所有能量需求 $e$ 互不相同，也不保证最小生成树唯一。

Output $m$ lines, each containing one integer: $E_{max}(c_i)$ for the $i$-th Corridor $c_i$ from the input.

输出 $m$ 行，每行包含一个整数：输入中第 $i$ 个走廊 $c_i$ 对应的 $E_{max}(c_i)$。