#include <bits/stdc++.h>
using namespace std;
#define FOR(i,k,n) for(int i = (k); i < (n); i++)
#define REP(i,n) FOR(i,0,n)
#define ALL(a) a.begin(), a.end()
#define MS(m,v) memset(m,v,sizeof(m))
#define D10 fixed<<setprecision(10)
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<string> vs;
typedef pair<int, int> pii;
const int MOD = 1000000007;
const int INF = MOD + 1;
const ld EPS = 1e-12;
template<class T> T &chmin(T &a, const T &b) { return a = min(a, b); }
template<class T> T &chmax(T &a, const T &b) { return a = max(a, b); }

/*--------------------template--------------------*/

typedef int Weight;
struct Edge
{
	int from, to; Weight cost;
	bool operator < (const Edge& e) const { return cost < e.cost; }
	bool operator > (const Edge& e) const { return cost > e.cost; }
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
typedef vector<Weight> Array;
typedef vector<Array> Matrix;
void add_edge(Graph &g, int from, int to, Weight cost)
{
	g[from].push_back(Edge{ from, to, cost });
}

pair<int, Edges> prim(Graph g)
{
	vector<bool> used(g.size());
	Edges res;
	int sum = 0;

	priority_queue<Edge, vector<Edge>, greater<Edge>> que;
	que.push(Edge{ -1, 0, 0 });

	while (!que.empty())
	{
		Edge e = que.top(); que.pop();
		if (used[e.to]) continue;
		if (e.from >= 0) res.push_back(e);
		sum += e.cost;
		used[e.to] = true;
		for (Edge i : g[e.to])
		{
			if (!used[i.to]) que.push(i);
		}
	}
	return make_pair(sum, res);
}

int main()
{
	int n, m;
	while (cin >> n >> m, n)
	{
		Graph g(n);
		REP(i, m)
		{
			int s, t, c; cin >> s >> t >> c;
			s--; t--;
			add_edge(g, s, t, c);
			add_edge(g, t, s, c);
		}
		Edges es = prim(g).second;
		sort(ALL(es));
		cout << es[n / 2 - 1].cost << endl;
	}
	return 0;
}
### 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;
#define FOR(i,k,n) for(int i = (k); i < (n); i++)
#define REP(i,n) FOR(i,0,n)
#define ALL(a) a.begin(), a.end()
#define MS(m,v) memset(m,v,sizeof(m))
#define D10 fixed<<setprecision(10)
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<string> vs;
typedef pair<int, int> pii;
const int MOD = 1000000007;
const int INF = MOD + 1;
const ld EPS = 1e-12;
template<class T> T &chmin(T &a, const T &b) { return a = min(a, b); }
template<class T> T &chmax(T &a, const T &b) { return a = max(a, b); }

/*--------------------template--------------------*/

typedef int Weight;
struct Edge
{
	int from, to; Weight cost;
	bool operator < (const Edge& e) const { return cost < e.cost; }
	bool operator > (const Edge& e) const { return cost > e.cost; }
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
typedef vector<Weight> Array;
typedef vector<Array> Matrix;
void add_edge(Graph &g, int from, int to, Weight cost)
{
	g[from].push_back(Edge{ from, to, cost });
}

pair<int, Edges> prim(Graph g)
{
	vector<bool> used(g.size());
	Edges res;
	int sum = 0;

	priority_queue<Edge, vector<Edge>, greater<Edge>> que;
	que.push(Edge{ -1, 0, 0 });

	while (!que.empty())
	{
		Edge e = que.top(); que.pop();
		if (used[e.to]) continue;
		if (e.from >= 0) res.push_back(e);
		sum += e.cost;
		used[e.to] = true;
		for (Edge i : g[e.to])
		{
			if (!used[i.to]) que.push(i);
		}
	}
	return make_pair(sum, res);
}

int main()
{
	int n, m;
	while (cin >> n >> m, n)
	{
		Graph g(n);
		REP(i, m)
		{
			int s, t, c; cin >> s >> t >> c;
			s--; t--;
			add_edge(g, s, t, c);
			add_edge(g, t, s, c);
		}
		Edges es = prim(g).second;
		sort(ALL(es));
		cout << es[n / 2 - 1].cost << endl;
	}
	return 0;
}
```