#include <iostream>
#include <cstdio>
#include <string>
#include <vector>
#include <algorithm>
using namespace std;

struct edge{
	int s, t, c;
	bool operator< (const edge &e) const{
		return c < e.c;
	}
} e[10000];

int par[10001];

int find(int x){
	return x != par[x] ? par[x] = find(par[x]) : x;
}

int main(){
	int n, m;
	while( scanf("%d%d", &n, &m) != EOF && n != 0 ){
		for(int i = 1; i <= n; ++i){
			par[i] = i;
		}
		for(int i = 0; i < m; ++i){
			scanf("%d%d%d", &e[i].s, &e[i].t, &e[i].c);
		}

		sort(e, e + m);

		int u = n / 2;
		for(int i = 0; i < m; ++i){
			int x = find(e[i].s);
			int y = find(e[i].t);
			if( x == y ) continue;
			par[x] = y;

			if( --u == 0 ){
				printf("%d\n", e[i].c);
				break;
			}
		}
	}
}
### Prompt

In Cpp, your task is to solve 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 <iostream>
#include <cstdio>
#include <string>
#include <vector>
#include <algorithm>
using namespace std;

struct edge{
	int s, t, c;
	bool operator< (const edge &e) const{
		return c < e.c;
	}
} e[10000];

int par[10001];

int find(int x){
	return x != par[x] ? par[x] = find(par[x]) : x;
}

int main(){
	int n, m;
	while( scanf("%d%d", &n, &m) != EOF && n != 0 ){
		for(int i = 1; i <= n; ++i){
			par[i] = i;
		}
		for(int i = 0; i < m; ++i){
			scanf("%d%d%d", &e[i].s, &e[i].t, &e[i].c);
		}

		sort(e, e + m);

		int u = n / 2;
		for(int i = 0; i < m; ++i){
			int x = find(e[i].s);
			int y = find(e[i].t);
			if( x == y ) continue;
			par[x] = y;

			if( --u == 0 ){
				printf("%d\n", e[i].c);
				break;
			}
		}
	}
}
```