#include <iostream>
#include <algorithm>
#include <vector>
#include <cassert>
using namespace std;

#define MAX (10010)

class UnionFind {
  
 private:
  int par[MAX];
  int rank[MAX];
  
 public:
  void init() {
    for(int i=0; i<MAX; i++) {
      par[i] = i;
      rank[i] = 0;
    }
  }
  
  int find(int x) {
    if(par[x] == x) { return x; }
    return par[x] = find(par[x]);
  }
  
  void unite(int x, int y) {
    x = find(x);
    y = find(y);
    
    if(x == y) return;
    
    if(rank[x] < rank[y]) {
      par[x] = y;
    } else {
      par[y] = x;
      if(rank[x] == rank[y]) rank[x] ++;
    }
  }
  
  bool same(int x, int y) { return find(x) == find(y); }

  UnionFind() { init(); }
};

struct Edge {
  int from, to, cost;
  Edge(int f=-1, int t=-1, int c=-1)
    : from(f), to(t), cost(c) {}
};

bool comp(const Edge& a, const Edge& b) {
  return a.cost < b.cost;
}

int kruskal(vector<Edge>& edges) {

  sort(edges.begin(), edges.end(), comp);
  UnionFind uf;
  vector<int> vec;
  for(int i=0; i<edges.size(); i++) {
    Edge e = edges[i];
    if(!uf.same(e.from, e.to)) {
      uf.unite(e.from, e.to);
      vec.push_back(edges[i].cost);
    }
  }
  sort(vec.begin(), vec.end());
  
  return vec[vec.size()/2];
}

int main() {
  
  int n, m;
  while(cin >> n >> m && (n|m)) {
    vector<Edge> es;
    for(int i=0; i<m; i++) {
      int s, t, c;
      cin >> s >> t >> c; s--, t--;
      es.push_back(Edge(s, t, c));
    }
    cout << kruskal(es) << endl;
  }
  
  return 0;
}
### Prompt

Please create a solution in CPP to the following problem:

Problem Statement

You are given a connected undirected graph which has even numbers of nodes. A connected graph is a graph in which all nodes are connected directly or indirectly by edges.

Your task is to find a spanning tree whose median value of edges' costs is minimum. A spanning tree of a graph means that a tree which contains all nodes of the graph.



Input

The input consists of multiple datasets.

The format of each dataset is as follows.


n m
s_1 t_1 c_1
...
s_m t_m c_m


The first line contains an even number n (2 \leq n \leq 1,000) and an integer m (n-1 \leq m \leq 10,000). n is the nubmer of nodes and m is the number of edges in the graph.

Then m lines follow, each of which contains s_i (1 \leq s_i \leq n), t_i (1 \leq s_i \leq n, t_i \neq s_i) and c_i (1 \leq c_i \leq 1,000). This means there is an edge between the nodes s_i and t_i and its cost is c_i. There is no more than one edge which connects s_i and t_i.

The input terminates when n=0 and m=0. Your program must not output anything for this case.

Output

Print the median value in a line for each dataset.

Example

Input

2 1
1 2 5
4 6
1 2 1
1 3 2
1 4 3
2 3 4
2 4 5
3 4 6
8 17
1 4 767
3 1 609
8 3 426
6 5 972
8 1 607
6 4 51
5 1 683
3 6 451
3 4 630
8 7 912
3 7 43
4 7 421
3 5 582
8 4 538
5 7 832
1 6 345
8 2 608
0 0


Output

5
2
421

### Response

```cpp
#include <iostream>
#include <algorithm>
#include <vector>
#include <cassert>
using namespace std;

#define MAX (10010)

class UnionFind {
  
 private:
  int par[MAX];
  int rank[MAX];
  
 public:
  void init() {
    for(int i=0; i<MAX; i++) {
      par[i] = i;
      rank[i] = 0;
    }
  }
  
  int find(int x) {
    if(par[x] == x) { return x; }
    return par[x] = find(par[x]);
  }
  
  void unite(int x, int y) {
    x = find(x);
    y = find(y);
    
    if(x == y) return;
    
    if(rank[x] < rank[y]) {
      par[x] = y;
    } else {
      par[y] = x;
      if(rank[x] == rank[y]) rank[x] ++;
    }
  }
  
  bool same(int x, int y) { return find(x) == find(y); }

  UnionFind() { init(); }
};

struct Edge {
  int from, to, cost;
  Edge(int f=-1, int t=-1, int c=-1)
    : from(f), to(t), cost(c) {}
};

bool comp(const Edge& a, const Edge& b) {
  return a.cost < b.cost;
}

int kruskal(vector<Edge>& edges) {

  sort(edges.begin(), edges.end(), comp);
  UnionFind uf;
  vector<int> vec;
  for(int i=0; i<edges.size(); i++) {
    Edge e = edges[i];
    if(!uf.same(e.from, e.to)) {
      uf.unite(e.from, e.to);
      vec.push_back(edges[i].cost);
    }
  }
  sort(vec.begin(), vec.end());
  
  return vec[vec.size()/2];
}

int main() {
  
  int n, m;
  while(cin >> n >> m && (n|m)) {
    vector<Edge> es;
    for(int i=0; i<m; i++) {
      int s, t, c;
      cin >> s >> t >> c; s--, t--;
      es.push_back(Edge(s, t, c));
    }
    cout << kruskal(es) << endl;
  }
  
  return 0;
}
```