#include<iostream>
#include<vector>
#include<string>
#include<algorithm>	
#include<map>
#include<set>
#include<utility>
#include<cmath>
#include<cstring>
#include<queue>
#include<stack>
#include<cstdio>
#include<sstream>
#include<iomanip>
#include<assert.h>
#define loop(i,a,b) for(int i=a;i<b;i++) 
#define rep(i,a) loop(i,0,a)
#define pb push_back
#define all(in) in.begin(),in.end()
#define shosu(x) fixed<<setprecision(x)
using namespace std;
//kaewasuretyuui
typedef long long ll;
typedef double Def;
typedef pair<Def,Def> pii;
typedef vector<Def> vi;
typedef vector<vi> vvi;
typedef vector<pii> vp;
typedef vector<vp> vvp;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef pair<Def,pii> pip;
typedef vector<pip>vip;
//#define mt make_tuple
//typedef tuple<int,string> tp;
//typedef vector<tp> vt;
const double PI=acos(-1);
const double EPS=1e-7;
const int inf=1e9;
const ll INF=2e18;
int dx[]={0,1,0,-1};
int dy[]={1,0,-1,0};
struct UnionFind{
    vector<int> data;
    UnionFind(int size) : data(size, -1) {}
    bool unionSet(int x,int y){
        x=root(x);y=root(y);
        if(x==y)return 0;
        if(data[y]<data[x])swap(x,y);
        data[x]+=data[y],data[y]=x;
        return 1;
    }
    bool findSet(int x,int y){
        return root(x)==root(y);
    }
    int root(int x){
        return data[x]<0 ? x : data[x]=root(data[x]);
    }
    int size(int x){
        return -data[root(x)];
    }
};
class KRK{//c++11
	public:
	struct edge{
		int from,to,cost;
	};
	vector<edge>G;
	int n;
	KRK(int size){
		n=size;
	}
	void add_edge(int a,int b,int c){
		edge e={a,b,c};
		G.pb(e);
	}
	int krk(){
		int sum=0;
		sort(all(G),[](edge a,edge b){
			return a.cost<b.cost;
		});
		UnionFind uf(n);
		int co=0;
		rep(i,G.size()){
			edge e=G[i];
			if(!uf.findSet(e.from,e.to)){
				sum+=e.cost;
				co++;
				if(co==n/2)cout<<e.cost<<endl;
				uf.unionSet(e.from,e.to);
			}
		}
		return sum;
	}
};
int main(){
	int n,m;
	while(cin>>n>>m,n){
		KRK krk(n);
		while(m--){
			int a,b,c;
			cin>>a>>b>>c;
			a--;b--;
			krk.add_edge(a,b,c);
		}
		krk.krk();
	}
}
### Prompt

Your challenge is to write 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<algorithm>	
#include<map>
#include<set>
#include<utility>
#include<cmath>
#include<cstring>
#include<queue>
#include<stack>
#include<cstdio>
#include<sstream>
#include<iomanip>
#include<assert.h>
#define loop(i,a,b) for(int i=a;i<b;i++) 
#define rep(i,a) loop(i,0,a)
#define pb push_back
#define all(in) in.begin(),in.end()
#define shosu(x) fixed<<setprecision(x)
using namespace std;
//kaewasuretyuui
typedef long long ll;
typedef double Def;
typedef pair<Def,Def> pii;
typedef vector<Def> vi;
typedef vector<vi> vvi;
typedef vector<pii> vp;
typedef vector<vp> vvp;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef pair<Def,pii> pip;
typedef vector<pip>vip;
//#define mt make_tuple
//typedef tuple<int,string> tp;
//typedef vector<tp> vt;
const double PI=acos(-1);
const double EPS=1e-7;
const int inf=1e9;
const ll INF=2e18;
int dx[]={0,1,0,-1};
int dy[]={1,0,-1,0};
struct UnionFind{
    vector<int> data;
    UnionFind(int size) : data(size, -1) {}
    bool unionSet(int x,int y){
        x=root(x);y=root(y);
        if(x==y)return 0;
        if(data[y]<data[x])swap(x,y);
        data[x]+=data[y],data[y]=x;
        return 1;
    }
    bool findSet(int x,int y){
        return root(x)==root(y);
    }
    int root(int x){
        return data[x]<0 ? x : data[x]=root(data[x]);
    }
    int size(int x){
        return -data[root(x)];
    }
};
class KRK{//c++11
	public:
	struct edge{
		int from,to,cost;
	};
	vector<edge>G;
	int n;
	KRK(int size){
		n=size;
	}
	void add_edge(int a,int b,int c){
		edge e={a,b,c};
		G.pb(e);
	}
	int krk(){
		int sum=0;
		sort(all(G),[](edge a,edge b){
			return a.cost<b.cost;
		});
		UnionFind uf(n);
		int co=0;
		rep(i,G.size()){
			edge e=G[i];
			if(!uf.findSet(e.from,e.to)){
				sum+=e.cost;
				co++;
				if(co==n/2)cout<<e.cost<<endl;
				uf.unionSet(e.from,e.to);
			}
		}
		return sum;
	}
};
int main(){
	int n,m;
	while(cin>>n>>m,n){
		KRK krk(n);
		while(m--){
			int a,b,c;
			cin>>a>>b>>c;
			a--;b--;
			krk.add_edge(a,b,c);
		}
		krk.krk();
	}
}
```