#include <bits/stdc++.h>
using namespace std;

struct UnionFind {
	vector<int> parent;
	
	UnionFind(int n){
		parent.resize(n);
		for (int i = 0; i < n; i++){
			parent[i] = i;
		}
	}
	
	int find(int x){
		if (parent[x] == x) return x;
		return parent[x] = find(parent[x]);
	}
	
	bool same(int x, int y){
		return find(x) == find(y);
	}
	
	bool unite(int x, int y){
		x = find(x);
		y = find(y);
		if (x == y) return false;
		parent[x] = y;
		return true;
	}
};


typedef tuple<int, int, int> Tp;
#define at(t, i) get<i>(t)

int n, m;

int main()
{
	while (scanf("%d %d", &n, &m), n){
		UnionFind uf(n);
		vector<Tp> es;
		vector<int> v;
		
		for (int i = 0; i < m; i++){
			int s, t, c;
			scanf("%d %d %d", &s, &t, &c);
			es.push_back(Tp(c, --s, --t));
		}
		
		sort(es.begin(), es.end());
		
		for (int i = 0; i < m; i++){
			if (uf.unite(at(es[i], 1), at(es[i], 2))){
				v.push_back(at(es[i], 0));
			}
		}
		
		int res = v[v.size() / 2];
		if (v.size() % 2 == 0){
			res += v[v.size() / 2 + 1];
		}
		
		printf("%d\n", res);
	}
}
### Prompt

Please formulate 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 <bits/stdc++.h>
using namespace std;

struct UnionFind {
	vector<int> parent;
	
	UnionFind(int n){
		parent.resize(n);
		for (int i = 0; i < n; i++){
			parent[i] = i;
		}
	}
	
	int find(int x){
		if (parent[x] == x) return x;
		return parent[x] = find(parent[x]);
	}
	
	bool same(int x, int y){
		return find(x) == find(y);
	}
	
	bool unite(int x, int y){
		x = find(x);
		y = find(y);
		if (x == y) return false;
		parent[x] = y;
		return true;
	}
};


typedef tuple<int, int, int> Tp;
#define at(t, i) get<i>(t)

int n, m;

int main()
{
	while (scanf("%d %d", &n, &m), n){
		UnionFind uf(n);
		vector<Tp> es;
		vector<int> v;
		
		for (int i = 0; i < m; i++){
			int s, t, c;
			scanf("%d %d %d", &s, &t, &c);
			es.push_back(Tp(c, --s, --t));
		}
		
		sort(es.begin(), es.end());
		
		for (int i = 0; i < m; i++){
			if (uf.unite(at(es[i], 1), at(es[i], 2))){
				v.push_back(at(es[i], 0));
			}
		}
		
		int res = v[v.size() / 2];
		if (v.size() % 2 == 0){
			res += v[v.size() / 2 + 1];
		}
		
		printf("%d\n", res);
	}
}
```