#include <bits/stdc++.h>
using namespace std;

#define int long long
#define REP(i, n) for ( int i = 0; i < (n); i++ )

template< typename T >
struct edge {
  int src, to;
  T cost;

  edge(int to, T cost) : src(-1), to(to), cost(cost) {}

  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};

template< typename T >
using Edges = vector< edge< T > >;
template< typename T >
using WeightedGraph = vector< Edges< T > >;
using UnWeightedGraph = vector< vector< int > >;
template< typename T >
using Matrix = vector< vector< T > >;

struct UnionFind {
  vector< int > data;
 
  UnionFind(int sz) {
    data.assign(sz, -1);
  }
 
  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if(x == y) return (false);
    if(data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return (true);
  }
 
  int find(int k) {
    if(data[k] < 0) return (k);
    return (data[k] = find(data[k]));
  }
 
  int size(int k) {
    return (-data[find(k)]);
  }
};

template< typename T >
T kruskal(Edges< T > &edges, int V) {  
  sort(begin(edges), end(edges), [](const edge< T > &a, const edge< T > &b) {
    return (a.cost < b.cost);
  });
  UnionFind tree(V);
  T ret = 0;
  int cnt = 0;
  int ans = 0;
  for(auto &e : edges) {
    if(tree.unite(e.src, e.to)) {
      cnt++;
      if ( cnt == V/2 ) ans = e.cost;      
      ret += e.cost;
    }
  }
  return (ans);
}

signed main() {
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(12);

  int n, m;
  while ( cin >> n >> m, n ) {
    Edges<int> E;
    for ( int i = 0; i < m; i++ ) {
      int s, t, c;
      cin >> s >> t >> c;
      s--; t--;
      E.push_back(edge<int>(s, t, c));      
    }

    cout << kruskal(E, n) << 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 <bits/stdc++.h>
using namespace std;

#define int long long
#define REP(i, n) for ( int i = 0; i < (n); i++ )

template< typename T >
struct edge {
  int src, to;
  T cost;

  edge(int to, T cost) : src(-1), to(to), cost(cost) {}

  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};

template< typename T >
using Edges = vector< edge< T > >;
template< typename T >
using WeightedGraph = vector< Edges< T > >;
using UnWeightedGraph = vector< vector< int > >;
template< typename T >
using Matrix = vector< vector< T > >;

struct UnionFind {
  vector< int > data;
 
  UnionFind(int sz) {
    data.assign(sz, -1);
  }
 
  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if(x == y) return (false);
    if(data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return (true);
  }
 
  int find(int k) {
    if(data[k] < 0) return (k);
    return (data[k] = find(data[k]));
  }
 
  int size(int k) {
    return (-data[find(k)]);
  }
};

template< typename T >
T kruskal(Edges< T > &edges, int V) {  
  sort(begin(edges), end(edges), [](const edge< T > &a, const edge< T > &b) {
    return (a.cost < b.cost);
  });
  UnionFind tree(V);
  T ret = 0;
  int cnt = 0;
  int ans = 0;
  for(auto &e : edges) {
    if(tree.unite(e.src, e.to)) {
      cnt++;
      if ( cnt == V/2 ) ans = e.cost;      
      ret += e.cost;
    }
  }
  return (ans);
}

signed main() {
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(12);

  int n, m;
  while ( cin >> n >> m, n ) {
    Edges<int> E;
    for ( int i = 0; i < m; i++ ) {
      int s, t, c;
      cin >> s >> t >> c;
      s--; t--;
      E.push_back(edge<int>(s, t, c));      
    }

    cout << kruskal(E, n) << endl;    
  }
  
  return 0;
}


```