F. K-th Pathtime limit per test2.5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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).OutputPrint 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).ExamplesInput
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
Output
3
Input
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
Output
9

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 
['brute force', 'constructive algorithms', 'shortest paths', 'sortings', '*2200']