#include <iostream>
#include <iomanip>
#include <cmath>
#include <cstdio>
#include <algorithm>
#include <vector>
#include <memory>
#include <cstring>
#include <cassert>
#include <numeric>
#include <sstream>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <cctype>
#include <unordered_map>
#include <unordered_set>
using namespace std;

#define REP2(i, m, n) for (int i = (int)(m); i < (int)(n); i++)
#define REP(i, n) REP2(i, 0, n)
#define ALL(S) (S).begin(), (S).end()
typedef long long ll;

class UnionFind{
  int num_components;
  std::vector<int> parent;
  std::vector<int> weight;
  std::vector<int> rank;
public:
  UnionFind(int N) : num_components(N),
                     parent(std::vector<int>(N)),
                     weight(std::vector<int>(N, 1)),
                     rank(std::vector<int>(N, 0)){
    for(int i = 0; i < N; i++) parent[i] = i;
  }
  
  int find(int x){
    if(x == parent[x]) return x;
    else return parent[x] = find(parent[x]);
  }
  
  int size(int x){
    return weight[find(x)];
  }

  
  bool same(int x, int y){
    return find(x) == find(y);
  }
    
  void unite(int x, int y){
    x = find(x);
    y = find(y);
    if(x == y) return;
    
    num_components--;
    if(rank[x] < rank[y]){
      weight[y] += weight[x];
      parent[x] = y;
    }else{
      weight[x] += weight[y];
      parent[y] = x;
      if(rank[x] == rank[y]) rank[y]++;
    }
  }
  
  int count(){
    return num_components;
  }
};


int main(){
  ios::sync_with_stdio(false);

  int n, m;
  while (cin >> n >> m && n + m){
    vector<tuple<int, int, int> > es;
    
    REP(i, m){
      int s, t, c;
      cin >> s >> t >> c;
      es.push_back(make_tuple(s - 1, t - 1, c));
    }
    
    int ub = 1010;
    int lb = -1;

    while (ub - lb > 1){
      int mb   = (lb + ub) >> 1;
      int cost = 0;

      UnionFind uf(n);

      REP(i, m) if (get<2>(es[i]) <= mb){
        uf.unite(get<0>(es[i]), get<1>(es[i]));
      }
      
      REP(i, m) if (get<2>(es[i]) > mb && !uf.same(get<0>(es[i]), get<1>(es[i]))){
          uf.unite(get<0>(es[i]), get<1>(es[i]));
        cost++;
      }

      if (cost * 2 > n - 1){
        lb = mb;
      } else {
        ub = mb;
      }
    }
    
    cout << ub << endl;
  }
  
  return 0;
}
### Prompt

Generate 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 <iostream>
#include <iomanip>
#include <cmath>
#include <cstdio>
#include <algorithm>
#include <vector>
#include <memory>
#include <cstring>
#include <cassert>
#include <numeric>
#include <sstream>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <cctype>
#include <unordered_map>
#include <unordered_set>
using namespace std;

#define REP2(i, m, n) for (int i = (int)(m); i < (int)(n); i++)
#define REP(i, n) REP2(i, 0, n)
#define ALL(S) (S).begin(), (S).end()
typedef long long ll;

class UnionFind{
  int num_components;
  std::vector<int> parent;
  std::vector<int> weight;
  std::vector<int> rank;
public:
  UnionFind(int N) : num_components(N),
                     parent(std::vector<int>(N)),
                     weight(std::vector<int>(N, 1)),
                     rank(std::vector<int>(N, 0)){
    for(int i = 0; i < N; i++) parent[i] = i;
  }
  
  int find(int x){
    if(x == parent[x]) return x;
    else return parent[x] = find(parent[x]);
  }
  
  int size(int x){
    return weight[find(x)];
  }

  
  bool same(int x, int y){
    return find(x) == find(y);
  }
    
  void unite(int x, int y){
    x = find(x);
    y = find(y);
    if(x == y) return;
    
    num_components--;
    if(rank[x] < rank[y]){
      weight[y] += weight[x];
      parent[x] = y;
    }else{
      weight[x] += weight[y];
      parent[y] = x;
      if(rank[x] == rank[y]) rank[y]++;
    }
  }
  
  int count(){
    return num_components;
  }
};


int main(){
  ios::sync_with_stdio(false);

  int n, m;
  while (cin >> n >> m && n + m){
    vector<tuple<int, int, int> > es;
    
    REP(i, m){
      int s, t, c;
      cin >> s >> t >> c;
      es.push_back(make_tuple(s - 1, t - 1, c));
    }
    
    int ub = 1010;
    int lb = -1;

    while (ub - lb > 1){
      int mb   = (lb + ub) >> 1;
      int cost = 0;

      UnionFind uf(n);

      REP(i, m) if (get<2>(es[i]) <= mb){
        uf.unite(get<0>(es[i]), get<1>(es[i]));
      }
      
      REP(i, m) if (get<2>(es[i]) > mb && !uf.same(get<0>(es[i]), get<1>(es[i]))){
          uf.unite(get<0>(es[i]), get<1>(es[i]));
        cost++;
      }

      if (cost * 2 > n - 1){
        lb = mb;
      } else {
        ub = mb;
      }
    }
    
    cout << ub << endl;
  }
  
  return 0;
}
```