A12865. 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 $j$ ( $1 \le i < j \le n$ ), then you need to print the $k$ -th element in the sorted array consisting of all $d_{i, j}$ , where $1 \le i < j \le n$ .

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).

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).