#include <cstdio>
#include <vector>
#include <algorithm>

#define rep(i,n) for(int i=0;i<(n);i++)

using namespace std;

class union_find{
	vector<int> a;
public:
	union_find(int n):a(n,-1){}
	int find(int x){
		if(a[x]<0) return x;
		return a[x]=find(a[x]);
	}
	void unite(int x,int y){
		x=find(x),y=find(y);
		if(x!=y){ a[x]+=a[y]; a[y]=x; }
	}
};

struct edge{
	int u,v,cost;
	bool operator<(const edge &e)const{ return cost<e.cost; }
};

int solve(int n,int m,edge *E){
	union_find U(n);
	sort(E,E+m);

	int cnt=0,res;
	rep(i,m) if(U.find(E[i].u)!=U.find(E[i].v)) {
		U.unite(E[i].u,E[i].v);
		cnt++;
		if(cnt==n/2){ res=E[i].cost; break; }
	}
	return res;
}

int main(){
	for(int n,m;scanf("%d%d",&n,&m),n;){
		edge E[10000];
		rep(i,m){
			int u,v,cost; scanf("%d%d%d",&u,&v,&cost); u--; v--;
			E[i]=(edge){u,v,cost};
		}
		printf("%d\n",solve(n,m,E));
	}
	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 <cstdio>
#include <vector>
#include <algorithm>

#define rep(i,n) for(int i=0;i<(n);i++)

using namespace std;

class union_find{
	vector<int> a;
public:
	union_find(int n):a(n,-1){}
	int find(int x){
		if(a[x]<0) return x;
		return a[x]=find(a[x]);
	}
	void unite(int x,int y){
		x=find(x),y=find(y);
		if(x!=y){ a[x]+=a[y]; a[y]=x; }
	}
};

struct edge{
	int u,v,cost;
	bool operator<(const edge &e)const{ return cost<e.cost; }
};

int solve(int n,int m,edge *E){
	union_find U(n);
	sort(E,E+m);

	int cnt=0,res;
	rep(i,m) if(U.find(E[i].u)!=U.find(E[i].v)) {
		U.unite(E[i].u,E[i].v);
		cnt++;
		if(cnt==n/2){ res=E[i].cost; break; }
	}
	return res;
}

int main(){
	for(int n,m;scanf("%d%d",&n,&m),n;){
		edge E[10000];
		rep(i,m){
			int u,v,cost; scanf("%d%d%d",&u,&v,&cost); u--; v--;
			E[i]=(edge){u,v,cost};
		}
		printf("%d\n",solve(n,m,E));
	}
	return 0;
}
```