#include<bits/stdc++.h>
using namespace std;
typedef vector<int> vi;

class UF{
  vi p,r;

public:
  UF(int n):p(n,-1),r(n,0){ }

  int find(int x){ return (p[x]<0)?x:(p[x] = find(p[x])); }

  void unite(int x,int y){
    x = find(x); y = find(y);
    if(x==y)return;

    if(r[x] < r[y])p[x] = y;
    else p[y] = x;
    if(r[x] == r[y])r[x]++;
  }

  bool same(int x,int y){return find(x)==find(y);}
};

const int INF= 1e9;

struct edge{
  int from, to, cost;
  edge(int x,int y, int z):from(x),to(y),cost(z){}
  bool operator<(const edge &x)const{ return cost<x.cost; }
};

class Kruskal{
  int n;
  vector< vector<edge> > g;
public:
  Kruskal(int a=0):n(a){ g.resize(n); }
  
  void AddEdge(int a, int b, int cost){
    g[a].push_back(edge(a,b,cost));
    g[b].push_back(edge(b,a,cost));
  }

  vector<edge> MinSpanningTree(){
    UF connect(n);
    vector<edge> edges;
    for(int v=0;v<n;v++){
      for(edge e : g[v])edges.push_back(e);
    }
    sort(edges.begin(), edges.end());
    
    vector<edge> res;
    for(edge e : edges){
      if(!connect.same(e.from,e.to)){
	res.push_back(e);
	connect.unite(e.from,e.to);
      }
    }
    return res;
  }
};

int main(){
  int n,m;
  while(cin >> n >> m, n){
    Kruskal mst(n);

    for(int i=0;i<m;i++){
      int s,t,c;
      cin >> s >> t >> c; s--; t--;
      mst.AddEdge(s,t,c);
    }
    vector<edge> res = mst.MinSpanningTree();
    cout << res[(n-1)/2].cost << endl;
  }
}
### Prompt

Please formulate a CPP solution 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<bits/stdc++.h>
using namespace std;
typedef vector<int> vi;

class UF{
  vi p,r;

public:
  UF(int n):p(n,-1),r(n,0){ }

  int find(int x){ return (p[x]<0)?x:(p[x] = find(p[x])); }

  void unite(int x,int y){
    x = find(x); y = find(y);
    if(x==y)return;

    if(r[x] < r[y])p[x] = y;
    else p[y] = x;
    if(r[x] == r[y])r[x]++;
  }

  bool same(int x,int y){return find(x)==find(y);}
};

const int INF= 1e9;

struct edge{
  int from, to, cost;
  edge(int x,int y, int z):from(x),to(y),cost(z){}
  bool operator<(const edge &x)const{ return cost<x.cost; }
};

class Kruskal{
  int n;
  vector< vector<edge> > g;
public:
  Kruskal(int a=0):n(a){ g.resize(n); }
  
  void AddEdge(int a, int b, int cost){
    g[a].push_back(edge(a,b,cost));
    g[b].push_back(edge(b,a,cost));
  }

  vector<edge> MinSpanningTree(){
    UF connect(n);
    vector<edge> edges;
    for(int v=0;v<n;v++){
      for(edge e : g[v])edges.push_back(e);
    }
    sort(edges.begin(), edges.end());
    
    vector<edge> res;
    for(edge e : edges){
      if(!connect.same(e.from,e.to)){
	res.push_back(e);
	connect.unite(e.from,e.to);
      }
    }
    return res;
  }
};

int main(){
  int n,m;
  while(cin >> n >> m, n){
    Kruskal mst(n);

    for(int i=0;i<m;i++){
      int s,t,c;
      cin >> s >> t >> c; s--; t--;
      mst.AddEdge(s,t,c);
    }
    vector<edge> res = mst.MinSpanningTree();
    cout << res[(n-1)/2].cost << endl;
  }
}
```