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

Input

The first line of the input contains three integers n, m and k (2 ≤ n ≤ 2 ⋅ 10^5, n - 1 ≤ m ≤ min\Big((n(n-1))/(2), 2 ⋅ 10^5\Big), 1 ≤ k ≤ min\Big((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 ≤ x, y ≤ n, 1 ≤ w ≤ 10^9, x ≠ 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
#include <bits/stdc++.h>
const long long INF = 1e18;
const double E = 1e-10;
const long long P = 1e9 + 7;
const long long Q = 31;
using namespace std;
void hello() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
void show(vector<long long>& arr) {
  for (auto i : arr) cout << i << " ";
  cout << "\n";
}
void show(vector<vector<long long>>& arr) {
  for (auto i : arr) show(i);
  cout << "\n";
}
struct edge {
  long long x, y, l;
  edge(){};
  edge(long long tx, long long ty, long long tl) {
    x = tx;
    y = ty;
    l = tl;
  }
};
long long cmp(edge l, edge r) { return l.l < r.l; }
signed main() {
  hello();
  long long n, m, k;
  cin >> n >> m >> k;
  vector<edge> graph;
  for (long long i = 0; i < m; ++i) {
    long long x, y, w;
    cin >> x >> y >> w;
    --x;
    --y;
    graph.push_back({x, y, w});
  }
  sort(graph.begin(), graph.end(), cmp);
  graph.resize(min(m, k));
  vector<long long> data;
  for (long long i = 0; i < graph.size(); ++i) {
    data.push_back(graph[i].x);
    data.push_back(graph[i].y);
  }
  sort(data.begin(), data.end());
  data.resize(unique(data.begin(), data.end()) - data.begin());
  vector<vector<pair<long long, long long>>> g(n);
  for (long long i = 0; i < graph.size(); ++i) {
    g[graph[i].x].push_back({graph[i].y, graph[i].l});
    g[graph[i].y].push_back({graph[i].x, graph[i].l});
  }
  vector<vector<long long>> res;
  for (auto st : data) {
    vector<long long> dist(n, INF);
    dist[st] = 0;
    set<pair<long long, long long>> mres;
    mres.insert({0, st});
    while (mres.size()) {
      long long v = mres.begin()->second;
      mres.erase(mres.begin());
      for (auto to : g[v]) {
        if (dist[to.first] > dist[v] + to.second) {
          mres.erase({dist[to.first], to.first});
          dist[to.first] = dist[v] + to.second;
          mres.insert({dist[to.first], to.first});
        }
      }
      if (mres.size()) {
        long long u = mres.begin()->second;
        res.push_back({mres.begin()->first, min(st, u), max(u, st)});
      }
    }
  }
  sort(res.begin(), res.end());
  unique(res.begin(), res.end());
  cout << res[k - 1][0] << "\n";
}
