#include <iostream>
#include <vector>
#include <queue>
#include <map>
#include <algorithm>
using namespace std;
typedef pair<int,int> P;
int main(){
	int n,m,s,t,c,i;
	for(;cin>>n>>m,n;){
		map<int,vector<P> >E;
		for(i=0;i<m;i++){
			cin>>s>>t>>c;
			E[s].push_back(make_pair(c,t));
			E[t].push_back(make_pair(c,s));
		}
		map<int,int>v;
		vector<int>a;
		priority_queue<P,vector<P>,greater<P> >Q;
		Q.push(make_pair(0,1));
		for(;!Q.empty();){
			P p=Q.top();Q.pop();
			if(!v[p.second]){
				v[p.second]=1;
				a.push_back(p.first);
				for(i=0;i<E[p.second].size();i++)Q.push(make_pair(E[p.second][i].first,E[p.second][i].second));
			}
		}
		sort(a.begin(),a.end());
		cout<<a[n/2]<<endl;
	}
}
### 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 <vector>
#include <queue>
#include <map>
#include <algorithm>
using namespace std;
typedef pair<int,int> P;
int main(){
	int n,m,s,t,c,i;
	for(;cin>>n>>m,n;){
		map<int,vector<P> >E;
		for(i=0;i<m;i++){
			cin>>s>>t>>c;
			E[s].push_back(make_pair(c,t));
			E[t].push_back(make_pair(c,s));
		}
		map<int,int>v;
		vector<int>a;
		priority_queue<P,vector<P>,greater<P> >Q;
		Q.push(make_pair(0,1));
		for(;!Q.empty();){
			P p=Q.top();Q.pop();
			if(!v[p.second]){
				v[p.second]=1;
				a.push_back(p.first);
				for(i=0;i<E[p.second].size();i++)Q.push(make_pair(E[p.second][i].first,E[p.second][i].second));
			}
		}
		sort(a.begin(),a.end());
		cout<<a[n/2]<<endl;
	}
}
```