#include<stdio.h>
#include<algorithm>
using namespace std;
int UF[1100];
int FIND(int a){
	if(UF[a]<0)return a;
	return UF[a]=FIND(UF[a]);
}
void UNION(int a,int b){
	a=FIND(a);b=FIND(b);if(a==b)return;
	UF[a]+=UF[b];UF[b]=a;
}
pair<int,pair<int,int> > edge[11000];
int main(){
	int a,b;
	while(scanf("%d%d",&a,&b),a){
		for(int i=0;i<b;i++){
			int p,q,r;scanf("%d%d%d",&p,&q,&r);
			p--;q--;
			edge[i]=make_pair(r,make_pair(p,q));
		}
		std::sort(edge,edge+b);
		for(int i=0;i<a;i++)UF[i]=-1;
		int cnt=a;
		for(int i=0;i<b;i++){
			if(FIND(edge[i].second.first)!=FIND(edge[i].second.second)){
				cnt--;
				UNION(edge[i].second.first,edge[i].second.second);
				if(cnt==a/2){
					printf("%d\n",edge[i].first);break;
				}
			}
		}
	}
}
### Prompt

Your challenge is to write 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<stdio.h>
#include<algorithm>
using namespace std;
int UF[1100];
int FIND(int a){
	if(UF[a]<0)return a;
	return UF[a]=FIND(UF[a]);
}
void UNION(int a,int b){
	a=FIND(a);b=FIND(b);if(a==b)return;
	UF[a]+=UF[b];UF[b]=a;
}
pair<int,pair<int,int> > edge[11000];
int main(){
	int a,b;
	while(scanf("%d%d",&a,&b),a){
		for(int i=0;i<b;i++){
			int p,q,r;scanf("%d%d%d",&p,&q,&r);
			p--;q--;
			edge[i]=make_pair(r,make_pair(p,q));
		}
		std::sort(edge,edge+b);
		for(int i=0;i<a;i++)UF[i]=-1;
		int cnt=a;
		for(int i=0;i<b;i++){
			if(FIND(edge[i].second.first)!=FIND(edge[i].second.second)){
				cnt--;
				UNION(edge[i].second.first,edge[i].second.second);
				if(cnt==a/2){
					printf("%d\n",edge[i].first);break;
				}
			}
		}
	}
}
```