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F. K-th Path

time limit per test

2.5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard 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 $$$1 \le i < j \le n$$$.

Input

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).

Output

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).

Examples

Input

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

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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