#include <bits/stdc++.h>

using namespace std;
using ll = long long;

class DisjointSets
{
public:
    DisjointSets(const int v)
    {
        m_parent.resize(v);
        m_rank.resize(v);
        m_size.resize(v);
        for (int i = 0; i < v; i++) {
            m_parent[i] = i;
            m_rank[i] = 0;
            m_size[i] = 1;
        }
    }

    bool same(const int a, const int b)
    {
        return find(a) == find(b);
    }


    int find(const int a)
    {
        if (m_parent[a] == a) {
            return a;
        } else {
            return m_parent[a] = find(m_parent[a]);
        }
    }

    void unite(const int a_, const int b_)
    {
        const int a = find(a_);
        const int b = find(b_);
        if (a == b) {
            return;
        }
        if (m_rank[a] > m_rank[b]) {
            m_parent[b] = a;
            m_size[a] += m_size[b];
        } else {
            m_parent[a] = b;
            m_size[b] += m_size[a];
        }
        if (m_rank[a] == m_rank[b]) {
            m_rank[b]++;
        }
    }

    int getSize(const int a)
    {
        return m_size[m_parent[a]];
    }

private:
    vector<int> m_parent;
    vector<int> m_rank;
    vector<int> m_size;
};

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    while (true) {
        int n, m;
        cin >> n >> m;
        if (n == 0 and m == 0) {
            break;
        }
        using P = pair<int, int>;
        vector<pair<int, P>> edge(m);
        for (int i = 0; i < m; i++) {
            int s, t, c;
            cin >> s >> t >> c;
            s--, t--;
            edge[i] = make_pair(c, make_pair(s, t));
        }
        sort(edge.begin(), edge.end());
        DisjointSets uf(n);
        vector<int> cost;
        for (int i = 0; i < m; i++) {
            const int c = edge[i].first;
            const int u = edge[i].second.first;
            const int v = edge[i].second.second;
            if (not uf.same(u, v)) {
                uf.unite(u, v);
                cost.push_back(c);
            }
        }
        cout << ((n - 1) % 2 == 1 ? cost[n / 2 - 1] : (cost[n / 2 - 1] + cost[n / 2]) * 1.0 / 2) << endl;
    }
    return 0;
}
### Prompt

Construct a CPP code solution to the problem outlined:

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;
using ll = long long;

class DisjointSets
{
public:
    DisjointSets(const int v)
    {
        m_parent.resize(v);
        m_rank.resize(v);
        m_size.resize(v);
        for (int i = 0; i < v; i++) {
            m_parent[i] = i;
            m_rank[i] = 0;
            m_size[i] = 1;
        }
    }

    bool same(const int a, const int b)
    {
        return find(a) == find(b);
    }


    int find(const int a)
    {
        if (m_parent[a] == a) {
            return a;
        } else {
            return m_parent[a] = find(m_parent[a]);
        }
    }

    void unite(const int a_, const int b_)
    {
        const int a = find(a_);
        const int b = find(b_);
        if (a == b) {
            return;
        }
        if (m_rank[a] > m_rank[b]) {
            m_parent[b] = a;
            m_size[a] += m_size[b];
        } else {
            m_parent[a] = b;
            m_size[b] += m_size[a];
        }
        if (m_rank[a] == m_rank[b]) {
            m_rank[b]++;
        }
    }

    int getSize(const int a)
    {
        return m_size[m_parent[a]];
    }

private:
    vector<int> m_parent;
    vector<int> m_rank;
    vector<int> m_size;
};

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    while (true) {
        int n, m;
        cin >> n >> m;
        if (n == 0 and m == 0) {
            break;
        }
        using P = pair<int, int>;
        vector<pair<int, P>> edge(m);
        for (int i = 0; i < m; i++) {
            int s, t, c;
            cin >> s >> t >> c;
            s--, t--;
            edge[i] = make_pair(c, make_pair(s, t));
        }
        sort(edge.begin(), edge.end());
        DisjointSets uf(n);
        vector<int> cost;
        for (int i = 0; i < m; i++) {
            const int c = edge[i].first;
            const int u = edge[i].second.first;
            const int v = edge[i].second.second;
            if (not uf.same(u, v)) {
                uf.unite(u, v);
                cost.push_back(c);
            }
        }
        cout << ((n - 1) % 2 == 1 ? cost[n / 2 - 1] : (cost[n / 2 - 1] + cost[n / 2]) * 1.0 / 2) << endl;
    }
    return 0;
}
```