#include <iostream>
#include <sstream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <cctype>
#include <cstring>
#include <string>
#include <vector>
#include <list>
#include <stack>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <bitset>
#include <numeric>
#include <complex>
#include <utility>
#include <iomanip>
#include <algorithm>
#include <functional>
using namespace std;

typedef vector<int> vint;
typedef vector<vint> vvint;
typedef vector<string> vst;
typedef pair<int,int> pint;
typedef long long ll;

#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define all(s) (s).begin(),(s).end()
#define each(i,s) for (typeof((s).begin()) i = (s).begin(); i != (s).end(); ++i)
#define debug(x) cout<<#x<<" = "<<(x)<<" (L"<<__LINE__<<")"<<endl
template<class T1, class T2> ostream& operator<<(ostream &s, pair<T1,T2> P){return s<<'<'<<P.first<<", "<<P.second<<'>';}
template<class T> ostream& operator<<(ostream &s, vector<T> P) {s<<"{ ";for(int i=0;i<P.size();++i){if(i>0)s<<", ";s<<P[i];}return s<<" }"<<endl;}
template<class T1, class T2> ostream& operator<<(ostream &s, map<T1,T2> P) {s<<"{ ";for(typeof(P.begin()) it=P.begin();it!=P.end();++it){if(it!=P.begin())s<<", ";s<<'<'<<it->first<<"->"<<it->second<<'>';}return s<<" }"<<endl;}



int n,m;

template<class T> struct Edge {
    int from, to;
    T cost;
    Edge(int f, int t, T c) : from(f), to(t), cost(c) {}
    friend bool operator < (const Edge &e1, const Edge &e2) {return e1.cost < e2.cost;}
    friend ostream& operator << (ostream& s, const Edge& E) {s << E.from << "->" << E.to << '(' << E.cost << ')';return s;}
};

const int MAX_V = 1050;
template<class T> struct Graph {
    static const int MAX_V_ = ::MAX_V;
    int V,E;
    vector<Edge<T> > list[MAX_V_];
    
    Graph(int n = 0) : V(n), E(0) {}
    void init(int n) {V = n; E = 0; for (int i = 0; i < MAX_V_; ++i) list[i].clear();}
    inline vector<Edge<T> >& operator [] (int i) {return list[i];}
    friend ostream& operator << (ostream& s, const Graph& G) {for (int i = 0; i < G.V; ++i) {s << i << " : " << G.list[i];}return s;}
    
    void connect(int f, int t, T c) {
        ++E;
        list[f].push_back(Edge<T>(f,t,c));
        list[t].push_back(Edge<T>(t,f,c));
    }
};

Graph<int> G;

struct UnionFind {    
    int size_;
    int par[MAX_V];
    int rank[MAX_V];
    
    UnionFind(int n = 0) {
        size_ = n;
        for (int i = 0; i < n; ++i) {
            par[i] = i;
            rank[i] = 0;
        }
    }
    
    void init(int n) {
        size_ = n;
        for (int i = 0; i < n; ++i) {
            par[i] = i;
            rank[i] = 0;
        }
    }
    
    int size() {return size_;}
    int root(int x) {return par[x] == x ? x : par[x] = root(par[x]);}    
    bool same(int x, int y) {return root(x) == root(y);}
    
    void connect(int x, int y) {
        x = root(x); 
        y = root(y);
        if (x == y) return;        
        if (rank[x] < rank[y]) par[x] = y;
        else {
            par[y] = x;
            if (rank[x] == rank[y]) ++rank[x];
        }
    }
    
};

vint tree;
UnionFind uf;

template<class T> void Kruskal(Graph<T> &G) {
    T res = 0.0;
    tree.clear();
    uf.init(G.V);
    vector<Edge<T> > edges;
    for (int v = 0; v < G.V; ++v) {
        for (int i = 0; i < G[v].size(); ++i) {
            edges.push_back(G[v][i]);
        }
    }
    sort(edges.begin(), edges.end());
    for (int i = 0; i < edges.size(); ++i) {
        Edge<T> e = edges[i];
        if (!uf.same(e.from, e.to)) {
            uf.connect(e.from, e.to);
            res += e.cost;
            tree.pb(e.cost);
        }
    }
}


int solve() {
    Kruskal(G);
    sort(all(tree));
    //debug(tree);
    return tree[(n-2)/2];
}

int main() {
    //freopen( "/Users/macuser/Documents/Programming/Contest/JAG Practice Asia 2012 C - Median Tree.in", "r", stdin );
    
    while (cin >> n >> m) {
        if (n == 0) break;
        G.init(n);
        for (int i = 0; i < m; ++i) {
            int s,t,c;
            cin >> s >> t >> c;
            G.connect(s-1, t-1, c);
        }
        //debug(G);
        cout << solve() << endl;
    }
    
    return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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 <sstream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <cctype>
#include <cstring>
#include <string>
#include <vector>
#include <list>
#include <stack>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <bitset>
#include <numeric>
#include <complex>
#include <utility>
#include <iomanip>
#include <algorithm>
#include <functional>
using namespace std;

typedef vector<int> vint;
typedef vector<vint> vvint;
typedef vector<string> vst;
typedef pair<int,int> pint;
typedef long long ll;

#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define all(s) (s).begin(),(s).end()
#define each(i,s) for (typeof((s).begin()) i = (s).begin(); i != (s).end(); ++i)
#define debug(x) cout<<#x<<" = "<<(x)<<" (L"<<__LINE__<<")"<<endl
template<class T1, class T2> ostream& operator<<(ostream &s, pair<T1,T2> P){return s<<'<'<<P.first<<", "<<P.second<<'>';}
template<class T> ostream& operator<<(ostream &s, vector<T> P) {s<<"{ ";for(int i=0;i<P.size();++i){if(i>0)s<<", ";s<<P[i];}return s<<" }"<<endl;}
template<class T1, class T2> ostream& operator<<(ostream &s, map<T1,T2> P) {s<<"{ ";for(typeof(P.begin()) it=P.begin();it!=P.end();++it){if(it!=P.begin())s<<", ";s<<'<'<<it->first<<"->"<<it->second<<'>';}return s<<" }"<<endl;}



int n,m;

template<class T> struct Edge {
    int from, to;
    T cost;
    Edge(int f, int t, T c) : from(f), to(t), cost(c) {}
    friend bool operator < (const Edge &e1, const Edge &e2) {return e1.cost < e2.cost;}
    friend ostream& operator << (ostream& s, const Edge& E) {s << E.from << "->" << E.to << '(' << E.cost << ')';return s;}
};

const int MAX_V = 1050;
template<class T> struct Graph {
    static const int MAX_V_ = ::MAX_V;
    int V,E;
    vector<Edge<T> > list[MAX_V_];
    
    Graph(int n = 0) : V(n), E(0) {}
    void init(int n) {V = n; E = 0; for (int i = 0; i < MAX_V_; ++i) list[i].clear();}
    inline vector<Edge<T> >& operator [] (int i) {return list[i];}
    friend ostream& operator << (ostream& s, const Graph& G) {for (int i = 0; i < G.V; ++i) {s << i << " : " << G.list[i];}return s;}
    
    void connect(int f, int t, T c) {
        ++E;
        list[f].push_back(Edge<T>(f,t,c));
        list[t].push_back(Edge<T>(t,f,c));
    }
};

Graph<int> G;

struct UnionFind {    
    int size_;
    int par[MAX_V];
    int rank[MAX_V];
    
    UnionFind(int n = 0) {
        size_ = n;
        for (int i = 0; i < n; ++i) {
            par[i] = i;
            rank[i] = 0;
        }
    }
    
    void init(int n) {
        size_ = n;
        for (int i = 0; i < n; ++i) {
            par[i] = i;
            rank[i] = 0;
        }
    }
    
    int size() {return size_;}
    int root(int x) {return par[x] == x ? x : par[x] = root(par[x]);}    
    bool same(int x, int y) {return root(x) == root(y);}
    
    void connect(int x, int y) {
        x = root(x); 
        y = root(y);
        if (x == y) return;        
        if (rank[x] < rank[y]) par[x] = y;
        else {
            par[y] = x;
            if (rank[x] == rank[y]) ++rank[x];
        }
    }
    
};

vint tree;
UnionFind uf;

template<class T> void Kruskal(Graph<T> &G) {
    T res = 0.0;
    tree.clear();
    uf.init(G.V);
    vector<Edge<T> > edges;
    for (int v = 0; v < G.V; ++v) {
        for (int i = 0; i < G[v].size(); ++i) {
            edges.push_back(G[v][i]);
        }
    }
    sort(edges.begin(), edges.end());
    for (int i = 0; i < edges.size(); ++i) {
        Edge<T> e = edges[i];
        if (!uf.same(e.from, e.to)) {
            uf.connect(e.from, e.to);
            res += e.cost;
            tree.pb(e.cost);
        }
    }
}


int solve() {
    Kruskal(G);
    sort(all(tree));
    //debug(tree);
    return tree[(n-2)/2];
}

int main() {
    //freopen( "/Users/macuser/Documents/Programming/Contest/JAG Practice Asia 2012 C - Median Tree.in", "r", stdin );
    
    while (cin >> n >> m) {
        if (n == 0) break;
        G.init(n);
        for (int i = 0; i < m; ++i) {
            int s,t,c;
            cin >> s >> t >> c;
            G.connect(s-1, t-1, c);
        }
        //debug(G);
        cout << solve() << endl;
    }
    
    return 0;
}

```