#include <bits/stdc++.h>
using namespace std;
#define int long long   // <-----!!!!!!!!!!!!!!!!!!!

#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n)-1;i>=0;i--)
#define rrep2(i,a,b) for (int i=(a)-1;i>=b;i--)
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define printV(_v) for(auto _x:_v){cout<<_x<<" ";}cout<<endl
#define printVS(vs) for(auto x : vs){cout << x << endl;}
#define printVV(_vv) for(auto _v:_vv){for(auto _x:_v){cout<<_x<<" ";}cout<<endl;}
#define printP(p) cout << p.first << " " << p.second << endl
#define printVP(vp) for(auto p : vp) printP(p);
#define readV(_v) rep(j, _v.size()) cin >> _v[j];
#define readVV(_vv) rep(i, _vv.size()) readV(_vv[i]);
#define output(_x) cout << _x << endl;

typedef long long ll;
typedef pair<int, int> Pii;
typedef tuple<int, int, int> TUPLE;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<Pii> vp;
const int inf = 1e9;
const int mod = 1e9 + 7;

template <typename T>
struct edge {
    int from, to;
    T cost;
    edge(){}
    edge(int _from, int _to, T _cost) : from(_from), to(_to), cost(_cost) {}
    bool operator< (const edge& e) const {
        return cost == e.cost ? (from == e.from ? to < e.to : from < e.from) : cost < e.cost;
    }
    bool operator> (const edge& e) const {
        return cost == e.cost ? (from == e.from ? to > e.to : from > e.from) : cost > e.cost;
    }
};

template <typename T>
class Prim {
private:
    const int n;
    vector<vector<edge<T>>> G;
public:
    Prim(int _n) : n(_n), G(_n) {}
    // undirected
    void addEdge(int u, int v, T c) {
        G[u].emplace_back(u, v, c);
        G[v].emplace_back(v, u, c);
    }
    T calc(int s = 0) {
        T total_weight = 0;
        vector<bool> visited(n);
        int num_visited = 0;
        priority_queue<edge<T>, vector<edge<T>>, greater<edge<T>>> pq;
        pq.push(edge<T>(-1, s, 0));
        vector<T> values;
        while (!pq.empty() && num_visited < n) {
            auto e = pq.top(); pq.pop();
            if (visited[e.to]) continue;
            total_weight += e.cost;
            values.emplace_back(e.cost);
            visited[e.to] = true;
            num_visited++;
            for (const auto& ne: G[e.to]) {
                if (!visited[ne.to]) pq.push(ne);
            }
        }
        sort(all(values));
        return values[1 + (values.size() - 1)/2];
    }
};
/* !!!!! T: ?????????????????????(int, double) !!!!! */

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

    int n, m;
    while (cin >> n >> m, n) {
        Prim<int> prim(n);
        rep(i, m) {
            int s, t, c;
            cin >> s >> t >> c;
            s--, t--;
            prim.addEdge(s, t, c);
        }
        cout << prim.calc() << endl;
    }
}
### Prompt

Please create a solution in Cpp 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 int long long   // <-----!!!!!!!!!!!!!!!!!!!

#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n)-1;i>=0;i--)
#define rrep2(i,a,b) for (int i=(a)-1;i>=b;i--)
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define printV(_v) for(auto _x:_v){cout<<_x<<" ";}cout<<endl
#define printVS(vs) for(auto x : vs){cout << x << endl;}
#define printVV(_vv) for(auto _v:_vv){for(auto _x:_v){cout<<_x<<" ";}cout<<endl;}
#define printP(p) cout << p.first << " " << p.second << endl
#define printVP(vp) for(auto p : vp) printP(p);
#define readV(_v) rep(j, _v.size()) cin >> _v[j];
#define readVV(_vv) rep(i, _vv.size()) readV(_vv[i]);
#define output(_x) cout << _x << endl;

typedef long long ll;
typedef pair<int, int> Pii;
typedef tuple<int, int, int> TUPLE;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<Pii> vp;
const int inf = 1e9;
const int mod = 1e9 + 7;

template <typename T>
struct edge {
    int from, to;
    T cost;
    edge(){}
    edge(int _from, int _to, T _cost) : from(_from), to(_to), cost(_cost) {}
    bool operator< (const edge& e) const {
        return cost == e.cost ? (from == e.from ? to < e.to : from < e.from) : cost < e.cost;
    }
    bool operator> (const edge& e) const {
        return cost == e.cost ? (from == e.from ? to > e.to : from > e.from) : cost > e.cost;
    }
};

template <typename T>
class Prim {
private:
    const int n;
    vector<vector<edge<T>>> G;
public:
    Prim(int _n) : n(_n), G(_n) {}
    // undirected
    void addEdge(int u, int v, T c) {
        G[u].emplace_back(u, v, c);
        G[v].emplace_back(v, u, c);
    }
    T calc(int s = 0) {
        T total_weight = 0;
        vector<bool> visited(n);
        int num_visited = 0;
        priority_queue<edge<T>, vector<edge<T>>, greater<edge<T>>> pq;
        pq.push(edge<T>(-1, s, 0));
        vector<T> values;
        while (!pq.empty() && num_visited < n) {
            auto e = pq.top(); pq.pop();
            if (visited[e.to]) continue;
            total_weight += e.cost;
            values.emplace_back(e.cost);
            visited[e.to] = true;
            num_visited++;
            for (const auto& ne: G[e.to]) {
                if (!visited[ne.to]) pq.push(ne);
            }
        }
        sort(all(values));
        return values[1 + (values.size() - 1)/2];
    }
};
/* !!!!! T: ?????????????????????(int, double) !!!!! */

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

    int n, m;
    while (cin >> n >> m, n) {
        Prim<int> prim(n);
        rep(i, m) {
            int s, t, c;
            cin >> s >> t >> c;
            s--, t--;
            prim.addEdge(s, t, c);
        }
        cout << prim.calc() << endl;
    }
}
```