#include<cstdio>
#include<algorithm>
using namespace std;
#define maxm 10010
#define maxn 1010
struct node 
{
	int u,v,w;
	bool ed;
	bool operator < (const node &rhs)const 
	{
		return w<rhs.w;
	}
}edge[maxm];
int fa[maxn],n,m;
int find(int x){return fa[x]==x?x:fa[x]=find(fa[x]);}
int main()
{
	while(~scanf("%d%d",&n,&m))
	{
		if(n==0&&m==0)break;
		for(int i=1;i<=n;i++)
			fa[i]=i;
		for(int i=1;i<=m;i++)
		{
			scanf("%d%d%d",&edge[i].u,&edge[i].v,&edge[i].w);
			edge[i].ed=0;
		}
		sort(edge+1,edge+m+1);
		int cnt=0,tmp=0,ans=0;
		for(int i=1;i<=m;i++)
		{
			int x=find(edge[i].u),y=find(edge[i].v);
			if(x==y)continue;
			fa[x]=y;
			edge[i].ed=1;
			cnt++;
		}
		for(int i=1;i<=m;i++)
		{
			if(edge[i].ed)
			{
				tmp++;
				if((cnt&1)&&tmp==(cnt+1)/2)
				{
					ans=edge[i].w;
					break;
				}
				if(cnt%2==0&&(tmp==cnt/2||tmp==cnt/2+1))
					ans+=edge[i].w;
				if(tmp>(cnt+1)/2+1)
					break;
			}
		}
		printf("%d\n",(cnt&1)?ans:ans/2);
	}
}
### 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<cstdio>
#include<algorithm>
using namespace std;
#define maxm 10010
#define maxn 1010
struct node 
{
	int u,v,w;
	bool ed;
	bool operator < (const node &rhs)const 
	{
		return w<rhs.w;
	}
}edge[maxm];
int fa[maxn],n,m;
int find(int x){return fa[x]==x?x:fa[x]=find(fa[x]);}
int main()
{
	while(~scanf("%d%d",&n,&m))
	{
		if(n==0&&m==0)break;
		for(int i=1;i<=n;i++)
			fa[i]=i;
		for(int i=1;i<=m;i++)
		{
			scanf("%d%d%d",&edge[i].u,&edge[i].v,&edge[i].w);
			edge[i].ed=0;
		}
		sort(edge+1,edge+m+1);
		int cnt=0,tmp=0,ans=0;
		for(int i=1;i<=m;i++)
		{
			int x=find(edge[i].u),y=find(edge[i].v);
			if(x==y)continue;
			fa[x]=y;
			edge[i].ed=1;
			cnt++;
		}
		for(int i=1;i<=m;i++)
		{
			if(edge[i].ed)
			{
				tmp++;
				if((cnt&1)&&tmp==(cnt+1)/2)
				{
					ans=edge[i].w;
					break;
				}
				if(cnt%2==0&&(tmp==cnt/2||tmp==cnt/2+1))
					ans+=edge[i].w;
				if(tmp>(cnt+1)/2+1)
					break;
			}
		}
		printf("%d\n",(cnt&1)?ans:ans/2);
	}
}
```