#include <iostream>
#include <vector>
#include <string>
#include <cmath>
#include <algorithm>
#include <utility>
#include <queue>
#include <set>
#include <map>

using namespace std;
typedef  long long ll;
typedef pair<int,int> PII;
typedef vector<int> VI;
typedef vector<VI> VVI;
#define  MP make_pair
#define  PB push_back
#define inf  1000000007
#define rep(i,n) for(int i=0;i<(int)(n);++i)

class UF {
private:
    int sz; vector<int> par,nrank;
public:
    UF(){}
    UF(int node_size){ sz = node_size; par.resize(sz),nrank.resize(sz); rep(i,sz){ par[i] = i; nrank[i] = 0; } }
    int find(int x){ if(par[x] == x){ return x; }else{ return par[x] = find(par[x]); } }
    void unite(int x,int y)
    { x = find(x),y = find(y); if(x == y) return;
    	if(nrank[x] < nrank[y]){ par[x] = y; }else{ par[y] = x; if(nrank[x] == nrank[y]) nrank[x]++; } }
    bool same(int x,int y){ return find(x) == find(y); }
};

template<typename T> class Kruskal{
public:
	struct edge{
		int u,v;
		T cost;
		bool operator<(const edge& another) const {
			return cost < another.cost;
		}
	};
	vector<edge> es;
	vector<int> par,rrank;
	int V;
    Kruskal(int node_size){
        V = node_size;
		par.resize(node_size), rrank.resize(node_size);
	}
	void add_edge(int u,int v,T cost){
		es.push_back((edge){u,v,cost});
	}
	void solve(){
		UF uf(V);
		T res = 0;
		int cnt = 0;
        sort(es.begin(),es.end());
		rep(i,es.size()){
			edge e = es[i];
			if(!uf.same(e.u,e.v)){
				uf.unite(e.u,e.v);
				res += e.cost;
				cnt++;
				if(cnt == V/2){
					cout << e.cost << endl;
					return;
				}
				if(cnt == V-1){
					break;
				}
			}
		}
		return;
	}
};


int main(){
	int n,m;
	
	while(cin >> n >> m&&n!=0){
		Kruskal<int> kr(n);
		rep(i,m){
			int s,t,c;
			cin >> s >> t >> c;
			s--;
			t--;
			kr.add_edge(s,t,c);
		}
		kr.solve();
	}
	return 0;
}
### Prompt

Your task is to create 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 <vector>
#include <string>
#include <cmath>
#include <algorithm>
#include <utility>
#include <queue>
#include <set>
#include <map>

using namespace std;
typedef  long long ll;
typedef pair<int,int> PII;
typedef vector<int> VI;
typedef vector<VI> VVI;
#define  MP make_pair
#define  PB push_back
#define inf  1000000007
#define rep(i,n) for(int i=0;i<(int)(n);++i)

class UF {
private:
    int sz; vector<int> par,nrank;
public:
    UF(){}
    UF(int node_size){ sz = node_size; par.resize(sz),nrank.resize(sz); rep(i,sz){ par[i] = i; nrank[i] = 0; } }
    int find(int x){ if(par[x] == x){ return x; }else{ return par[x] = find(par[x]); } }
    void unite(int x,int y)
    { x = find(x),y = find(y); if(x == y) return;
    	if(nrank[x] < nrank[y]){ par[x] = y; }else{ par[y] = x; if(nrank[x] == nrank[y]) nrank[x]++; } }
    bool same(int x,int y){ return find(x) == find(y); }
};

template<typename T> class Kruskal{
public:
	struct edge{
		int u,v;
		T cost;
		bool operator<(const edge& another) const {
			return cost < another.cost;
		}
	};
	vector<edge> es;
	vector<int> par,rrank;
	int V;
    Kruskal(int node_size){
        V = node_size;
		par.resize(node_size), rrank.resize(node_size);
	}
	void add_edge(int u,int v,T cost){
		es.push_back((edge){u,v,cost});
	}
	void solve(){
		UF uf(V);
		T res = 0;
		int cnt = 0;
        sort(es.begin(),es.end());
		rep(i,es.size()){
			edge e = es[i];
			if(!uf.same(e.u,e.v)){
				uf.unite(e.u,e.v);
				res += e.cost;
				cnt++;
				if(cnt == V/2){
					cout << e.cost << endl;
					return;
				}
				if(cnt == V-1){
					break;
				}
			}
		}
		return;
	}
};


int main(){
	int n,m;
	
	while(cin >> n >> m&&n!=0){
		Kruskal<int> kr(n);
		rep(i,m){
			int s,t,c;
			cin >> s >> t >> c;
			s--;
			t--;
			kr.add_edge(s,t,c);
		}
		kr.solve();
	}
	return 0;
}
```