K-th Path

### 题目描述 给定一个无向带权连通图，求子节点两两之间最短路径长度从小到大排序之后第 $k$ 长的路径长度。 ### 输入格式 第一行三个整数 $n,m,k$。共有 $n$ 个结点，$m$ 条**双向**边，求第 $k$ 长的路径。 之后 $m$ 行，每行三个整数 $x,y,w(x\neq y)$，表示 $x,y$ 之间有一条长为 $w$ 的**双向**边。 ### 输出格式 一个整数，即子节点两两之间最短路径长度从小到大排序之后第 $k$ 长的路径长度。 ### 提示与说明 对于 $100\%$ 的数据，$ 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),1\le w\le 10^9$。

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).

6 10 5
2 5 1
5 3 9
6 2 2
1 3 1
5 1 8
6 5 10
1 6 5
6 4 6
3 6 2
3 4 5

3

7 15 18
2 6 3
5 7 4
6 5 4
3 6 9
6 7 7
1 6 4
7 1 6
7 2 1
4 3 2
3 2 8
5 3 6
2 5 5
3 7 9
4 1 8
2 1 1

9