// {{{ include
#include <cstdio>
#include <cmath>
#include <cstring>
#include <iostream>
#include <vector>
#include <string>
#include <set>
#include <map>
#include <queue>
#include <algorithm>
// }}}
#include <climits>

//{{{ uf.hpp
#ifndef INCLUDE_UF_HPP
#define INCLUDE_UF_HPP
#include <vector>
#include <algorithm>
namespace orliv {
//{{{ UF merge, same, root, size, count
struct UF {
  std::vector<int> data;
  int cnt;
  UF(int n) : data(n, -1), cnt(n) {}
  bool merge(int a, int b){
    a = root(a);
    b = root(b);
    if (a != b){
      cnt--;
      if (data[b] < data[a]) std::swap(a, b);
      data[a] += data[b];
      data[b] = a;
    }
    return a != b;
  }
  bool same(int a, int b){ return root(a) == root(b); }
  int root(int a){ return data[a] >= 0 ? data[a] = root(data[a]) : a; }
  int size(int a){ return -data[root(a)]; }
  int count(){ return cnt; }
};
//}}}
}
#endif
//}}}
//{{{ graph.hpp
#ifndef INCLUDE_GRAPH_HPP
#define INCLUDE_GRAPH_HPP
#include <vector>
namespace orliv {
struct Edge {
  typedef int weight_t;
  int from, to;
  weight_t w;
  Edge(int from, int to, weight_t w) : from(from), to(to), w(w) {}
  bool operator<(const Edge& e) const {
    return w != e.w ? w > e.w : from != e.from ? from < e.from : to < e.to;
  }
  static const weight_t INF;
};
const int Edge::INF=INT_MAX;
typedef std::vector<Edge> Edges;
typedef std::vector<Edges> Graph;
}
#endif
//}}}

using namespace std;
using namespace orliv;

//{{{ Edges kruskal(g)
Edges kruskal(const Graph& g){
  const int V = g.size();
  int E = 0;
  for (const auto& v : g) E += v.size();
  Edges es;
  es.reserve(E);
  for (const auto& v : g){
    for (const auto& e : v){
      es.emplace_back(e);
    }
  }
  sort(es.begin(), es.end());
  reverse(es.begin(), es.end());
  UF uf(V);
  Edges result;
  for (const auto& e : es){
    if (uf.same(e.from, e.to)) continue;
    uf.merge(e.from, e.to);
    result.emplace_back(e);
  }
  return result;
}
//}}}

typedef long long ll;
inline int in(){int x;scanf("%d",&x);return x;}

int main()
{
  int N, M;
  while (N = in(), M = in()){
    Graph G(N);
    for (int i = 0; i < M; i++){
      int s = in() - 1, t = in() - 1, c = in();
      G[s].emplace_back(s, t, c);
      G[t].emplace_back(t, s, c);
    }
    Edges stree = kruskal(G);
    cout << stree[N / 2 - 1].w << 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
#include <cstdio>
#include <cmath>
#include <cstring>
#include <iostream>
#include <vector>
#include <string>
#include <set>
#include <map>
#include <queue>
#include <algorithm>
// }}}
#include <climits>

//{{{ uf.hpp
#ifndef INCLUDE_UF_HPP
#define INCLUDE_UF_HPP
#include <vector>
#include <algorithm>
namespace orliv {
//{{{ UF merge, same, root, size, count
struct UF {
  std::vector<int> data;
  int cnt;
  UF(int n) : data(n, -1), cnt(n) {}
  bool merge(int a, int b){
    a = root(a);
    b = root(b);
    if (a != b){
      cnt--;
      if (data[b] < data[a]) std::swap(a, b);
      data[a] += data[b];
      data[b] = a;
    }
    return a != b;
  }
  bool same(int a, int b){ return root(a) == root(b); }
  int root(int a){ return data[a] >= 0 ? data[a] = root(data[a]) : a; }
  int size(int a){ return -data[root(a)]; }
  int count(){ return cnt; }
};
//}}}
}
#endif
//}}}
//{{{ graph.hpp
#ifndef INCLUDE_GRAPH_HPP
#define INCLUDE_GRAPH_HPP
#include <vector>
namespace orliv {
struct Edge {
  typedef int weight_t;
  int from, to;
  weight_t w;
  Edge(int from, int to, weight_t w) : from(from), to(to), w(w) {}
  bool operator<(const Edge& e) const {
    return w != e.w ? w > e.w : from != e.from ? from < e.from : to < e.to;
  }
  static const weight_t INF;
};
const int Edge::INF=INT_MAX;
typedef std::vector<Edge> Edges;
typedef std::vector<Edges> Graph;
}
#endif
//}}}

using namespace std;
using namespace orliv;

//{{{ Edges kruskal(g)
Edges kruskal(const Graph& g){
  const int V = g.size();
  int E = 0;
  for (const auto& v : g) E += v.size();
  Edges es;
  es.reserve(E);
  for (const auto& v : g){
    for (const auto& e : v){
      es.emplace_back(e);
    }
  }
  sort(es.begin(), es.end());
  reverse(es.begin(), es.end());
  UF uf(V);
  Edges result;
  for (const auto& e : es){
    if (uf.same(e.from, e.to)) continue;
    uf.merge(e.from, e.to);
    result.emplace_back(e);
  }
  return result;
}
//}}}

typedef long long ll;
inline int in(){int x;scanf("%d",&x);return x;}

int main()
{
  int N, M;
  while (N = in(), M = in()){
    Graph G(N);
    for (int i = 0; i < M; i++){
      int s = in() - 1, t = in() - 1, c = in();
      G[s].emplace_back(s, t, c);
      G[t].emplace_back(t, s, c);
    }
    Edges stree = kruskal(G);
    cout << stree[N / 2 - 1].w << endl;
  }

  return 0;
}
```