#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#define inf 0x3f3f3f3f
using namespace std;
int ma[1010][1010];
int cost[1010],a[1010]; 
int n,m;
void init(){
	for(int i=1;i<=n;i++){
		for(int j=1;j<i;j++)
			ma[i][j]=ma[j][i]=inf;
		ma[i][i]=0;
	}
	memset(a,0,sizeof(a));
}
int prim(int s){
	int i,j;
	int k=0;
	for(i=1;i<=n;i++)
		cost[i]=ma[s][i];
	int sum=0;
	int mini;
	for(i=1;i<n;i++){
		mini=inf;
		for(j=1;j<=n;j++)
			if(cost[j]<mini&&cost[j]!=0){
				s=j;
				mini=cost[j];
			}
			sum+=mini;
			cost[s]=0;
			a[k++]=mini;
			for(j=1;j<=n;j++)
				if(cost[j]>ma[s][j]&&ma[s][j]!=0)
					cost[j]=ma[s][j];
	}
	sort(a,a+k);
	return a[k/2];
}
int main(){
	int from,to,cost;
	while(scanf("%d%d",&n,&m)&&(n+m)!=0){
		init();
		for(int i=1;i<=m;i++){
			scanf("%d%d%d",&from,&to,&cost);
			ma[from][to]=ma[to][from]=cost;
		}
		printf("%d\n",prim(1));
	}
	return 0;
}
### 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<cstring>
#include<cstdio>
#include<algorithm>
#define inf 0x3f3f3f3f
using namespace std;
int ma[1010][1010];
int cost[1010],a[1010]; 
int n,m;
void init(){
	for(int i=1;i<=n;i++){
		for(int j=1;j<i;j++)
			ma[i][j]=ma[j][i]=inf;
		ma[i][i]=0;
	}
	memset(a,0,sizeof(a));
}
int prim(int s){
	int i,j;
	int k=0;
	for(i=1;i<=n;i++)
		cost[i]=ma[s][i];
	int sum=0;
	int mini;
	for(i=1;i<n;i++){
		mini=inf;
		for(j=1;j<=n;j++)
			if(cost[j]<mini&&cost[j]!=0){
				s=j;
				mini=cost[j];
			}
			sum+=mini;
			cost[s]=0;
			a[k++]=mini;
			for(j=1;j<=n;j++)
				if(cost[j]>ma[s][j]&&ma[s][j]!=0)
					cost[j]=ma[s][j];
	}
	sort(a,a+k);
	return a[k/2];
}
int main(){
	int from,to,cost;
	while(scanf("%d%d",&n,&m)&&(n+m)!=0){
		init();
		for(int i=1;i<=m;i++){
			scanf("%d%d%d",&from,&to,&cost);
			ma[from][to]=ma[to][from]=cost;
		}
		printf("%d\n",prim(1));
	}
	return 0;
}
```