CF1196F.K-th Path

You are given a connected undirected weighted graph consisting of $n$ vertices and $m$ edges.

You need to print the $k$-th smallest shortest path in this graph (paths from the vertex to itself are not counted, paths from $i$ to $j$ and from $j$ to $i$ are counted as one).

More formally, if $d$ is the matrix of shortest paths, where $d_{i, j}$ is the length of the shortest path between vertices $i$ and $j$ ($1 \le i \lt j \le n$), then you need to print the $k$-th element in the sorted array consisting of all $d_{i, j}$, where $1 \le i \lt j \le n$.

给你一个包含 $n$ 个顶点和 $m$ 条边的连通无向带权图。

你需要输出该图中第 $k$ 小的最短路径长度（不考虑从某顶点到其自身的路径；从顶点 $i$ 到 $j$ 的路径与从 $j$ 到 $i$ 的路径视为同一条路径）。

更准确地说，设 $d$ 为最短路径距离矩阵，其中 $d_{i, j}$ 表示顶点 $i$ 与 $j$ 之间的最短路径长度（$1 \le i \lt j \le n$），则你需要输出由所有满足 $1 \le i \lt j \le n$ 的 $d_{i, j}$ 构成的数组经升序排序后的第 $k$ 个元素。

The first line of the input contains three integers $n, m$ and $k$ ($2 \le n \le 2 \cdot 10^5$, $n - 1 \le m \le \min\Big(\frac{n(n-1)}{2}, 2 \cdot 10^5\Big)$, $1 \le k \le \min\Big(\frac{n(n-1)}{2}, 400\Big)$ — the number of vertices in the graph, the number of edges in the graph and the value of $k$, correspondingly.

Then $m$ lines follow, each containing three integers $x$, $y$ and $w$ ($1 \le x, y \le n$, $1 \le w \le 10^9$, $x \ne y$) denoting an edge between vertices $x$ and $y$ of weight $w$.

It is guaranteed that the given graph is connected (there is a path between any pair of vertices), there are no self-loops (edges connecting the vertex with itself) and multiple edges (for each pair of vertices $x$ and $y$, there is at most one edge between this pair of vertices in the graph).

输入的第一行包含三个整数 $n$、$m$ 和 $k$（$2 \le n \le 2 \cdot 10^5$，$n - 1 \le m \le \min\Big(\frac{n(n-1)}{2}, 2 \cdot 10^5\Big)$，$1 \le k \le \min\Big(\frac{n(n-1)}{2}, 400\Big)$），分别表示图中顶点的数量、边的数量以及参数 $k$ 的值。

接下来是 $m$ 行，每行包含三个整数 $x$、$y$ 和 $w$（$1 \le x, y \le n$，$1 \le w \le 10^9$，$x \ne y$），表示一条连接顶点 $x$ 与 $y$、权重为 $w$ 的边。

保证所给图是连通的（任意两个顶点之间均存在路径），且图中不存在自环（即没有连接顶点与其自身的边）和重边（即对任意一对顶点 $x$ 和 $y$，图中至多只有一条连接它们的边）。

Print one integer — the length of the $k$-th smallest shortest path in the given graph (paths from the vertex to itself are not counted, paths from $i$ to $j$ and from $j$ to $i$ are counted as one).

输出一个整数——给定图中第 $k$ 小的最短路径的长度（不考虑从某顶点到其自身的路径；从顶点 $i$ 到 $j$ 的路径与从 $j$ 到 $i$ 的路径被视为同一条路径）。