#include  <bits/stdc++.h>
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
using namespace std;

const int vmax=10010;
const int inf=1023456789;

int N,M;
typedef tuple<int,int,int> node;
vector<node> graph;

int par[vmax];
void init(){rep(i,vmax) par[i]=i;}
int find(int x){return (par[x]==x)?x:par[x]=find(par[x]);}
void unite(int a,int b){a=find(a),b=find(b);par[a]=b;}
bool same(int a,int b){return find(a)==find(b);}

int kruskal(){
	init();
	sort(begin(graph),end(graph));
	int res=inf,num=0;
	for(auto &e:graph){
		int a,b,c;
		tie(c,a,b)=e;
		if(!same(a,b)) unite(a,b),num++;
		if(num==N/2) res=min(res,c);
	}
	return res;
}

int main(void){
	while(cin >> N >> M,N){
		graph.clear();
		rep(i,M){
			int a,b,c;
			cin >> a >> b >> c;
			graph.push_back(node(c,a,b));
		}
		cout << kruskal() << endl;
	}
	return 0;
}
### Prompt

Create a solution in cpp for 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>
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
using namespace std;

const int vmax=10010;
const int inf=1023456789;

int N,M;
typedef tuple<int,int,int> node;
vector<node> graph;

int par[vmax];
void init(){rep(i,vmax) par[i]=i;}
int find(int x){return (par[x]==x)?x:par[x]=find(par[x]);}
void unite(int a,int b){a=find(a),b=find(b);par[a]=b;}
bool same(int a,int b){return find(a)==find(b);}

int kruskal(){
	init();
	sort(begin(graph),end(graph));
	int res=inf,num=0;
	for(auto &e:graph){
		int a,b,c;
		tie(c,a,b)=e;
		if(!same(a,b)) unite(a,b),num++;
		if(num==N/2) res=min(res,c);
	}
	return res;
}

int main(void){
	while(cin >> N >> M,N){
		graph.clear();
		rep(i,M){
			int a,b,c;
			cin >> a >> b >> c;
			graph.push_back(node(c,a,b));
		}
		cout << kruskal() << endl;
	}
	return 0;
}
```