#define _CRT_SECURE_NO_WARNINGS
//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int,int> pii;
#define all(c) (c).begin(), (c).end()
#define loop(i,a,b) for(ll i=a; i<ll(b); i++)
#define rep(i,b) loop(i,0,b)
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
template<class T> istream& operator>>(istream& is, vector<T>& v);
template<class T> ostream& operator<<(ostream& os, vector<T> const& v);
template<int n, class...T> typename enable_if<(n>=sizeof...(T))>::type _ot(ostream&, const tuple<T...>&){}
template<int n, class...T> typename enable_if<(n< sizeof...(T))>::type _ot(ostream& os, const tuple<T...>& t){ os << (n==0?"":" ") << get<n>(t); _ot<n+1>(os, t); }
template<class...T> ostream& operator<<(ostream& os, const tuple<T...>& t){ _ot<0>(os, t); return os; }
template<int n, class...T> typename enable_if<(n>=sizeof...(T))>::type _it(istream&, tuple<T...>&){}
template<int n, class...T> typename enable_if<(n< sizeof...(T))>::type _it(istream& is, tuple<T...>& t){ is >> get<n>(t); _it<n+1>(is, t); }
template<class...T> istream& operator>>(istream& is, tuple<T...>& t){ _it<0>(is, t); return is; }
template<class T> istream& operator>>(istream& is, vector<T>& v){ rep(i,v.size()) is >> v[i]; return is; }
template<class T> ostream& operator<<(ostream& os, vector<T> const& v){ rep(i,v.size()) os << v[i] << (i+1==(int)v.size()?"":" "); return os; }
#ifdef DEBUG
#define dump(...) (cerr<<#__VA_ARGS__<<" = "<<mt(__VA_ARGS__)<<" ["<<__LINE__<<"]"<<endl)
#else
#define dump(...)
#endif

// グラフ用ヘッダ

typedef int Weight;
struct Edge {
    int src, dst;
    Weight weight;
    Edge(int src, int dst, Weight weight) :
        src(src), dst(dst), weight(weight) { }
};
bool operator < (const Edge &e, const Edge &f) {
    return e.weight != f.weight ? e.weight > f.weight : // !!INVERSE!!
        e.src != f.src ? e.src < f.src : e.dst < f.dst;
}
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

typedef vector<Weight> Array;
typedef vector<Array> Matrix;

struct UnionFind {
    vector<int> data;
    int cnt;
    UnionFind(int size) : data(size, -1), cnt(size) { }
    // 併合
    bool set(int x, int y) {
        x = root(x); y = root(y);
        if (x != y) {
            if (data[y] < data[x]) swap(x, y);
            data[x] += data[y]; data[y] = x;
        }
        if(x != y) cnt--;
        return x != y;
    }
    // 判定
    bool ask(int x, int y) {
        return root(x) == root(y);
    }
    // 根
    int root(int x) {
        return data[x] < 0 ? x : data[x] = root(data[x]);
    }
    // xが属する集合の位数
    int size(int x) {
        return -data[root(x)];
    }
    // 集合の数
    int size() {
        return cnt;
    }
};

pair<Weight, Edges> kruskal(Graph const& g){
    int n = g.size();
    UnionFind uf(n+1);
    Edges es;
    rep(u, n) rep(i,g[u].size()) if (u < g[u][i].dst) es.push_back(g[u][i]);
    sort(all(es)); // !! INVERSE !!
    reverse(all(es));
    Weight total = 0;
    Edges res;
    for(auto const & e : es){
        if(!uf.ask(e.src,e.dst)){
            res.push_back(e);
            total += e.weight;
            uf.set(e.src,e.dst);
        }
    }
    return make_pair(total,res);
}

int main(){
    int n,m;
    while(cin>>n>>m && n){
        Graph g(n+1);
        rep(i,m){
            int a,b,c; cin >> a >> b >> c;
            g[a].eb(a,b,c); g[b].eb(b,a,c);
        }
        auto res = kruskal(g).second;
        cout << res[n/2-1].weight << endl;
    }
}
### Prompt

Create a solution in CPP for 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
#define _CRT_SECURE_NO_WARNINGS
//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int,int> pii;
#define all(c) (c).begin(), (c).end()
#define loop(i,a,b) for(ll i=a; i<ll(b); i++)
#define rep(i,b) loop(i,0,b)
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
template<class T> istream& operator>>(istream& is, vector<T>& v);
template<class T> ostream& operator<<(ostream& os, vector<T> const& v);
template<int n, class...T> typename enable_if<(n>=sizeof...(T))>::type _ot(ostream&, const tuple<T...>&){}
template<int n, class...T> typename enable_if<(n< sizeof...(T))>::type _ot(ostream& os, const tuple<T...>& t){ os << (n==0?"":" ") << get<n>(t); _ot<n+1>(os, t); }
template<class...T> ostream& operator<<(ostream& os, const tuple<T...>& t){ _ot<0>(os, t); return os; }
template<int n, class...T> typename enable_if<(n>=sizeof...(T))>::type _it(istream&, tuple<T...>&){}
template<int n, class...T> typename enable_if<(n< sizeof...(T))>::type _it(istream& is, tuple<T...>& t){ is >> get<n>(t); _it<n+1>(is, t); }
template<class...T> istream& operator>>(istream& is, tuple<T...>& t){ _it<0>(is, t); return is; }
template<class T> istream& operator>>(istream& is, vector<T>& v){ rep(i,v.size()) is >> v[i]; return is; }
template<class T> ostream& operator<<(ostream& os, vector<T> const& v){ rep(i,v.size()) os << v[i] << (i+1==(int)v.size()?"":" "); return os; }
#ifdef DEBUG
#define dump(...) (cerr<<#__VA_ARGS__<<" = "<<mt(__VA_ARGS__)<<" ["<<__LINE__<<"]"<<endl)
#else
#define dump(...)
#endif

// グラフ用ヘッダ

typedef int Weight;
struct Edge {
    int src, dst;
    Weight weight;
    Edge(int src, int dst, Weight weight) :
        src(src), dst(dst), weight(weight) { }
};
bool operator < (const Edge &e, const Edge &f) {
    return e.weight != f.weight ? e.weight > f.weight : // !!INVERSE!!
        e.src != f.src ? e.src < f.src : e.dst < f.dst;
}
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

typedef vector<Weight> Array;
typedef vector<Array> Matrix;

struct UnionFind {
    vector<int> data;
    int cnt;
    UnionFind(int size) : data(size, -1), cnt(size) { }
    // 併合
    bool set(int x, int y) {
        x = root(x); y = root(y);
        if (x != y) {
            if (data[y] < data[x]) swap(x, y);
            data[x] += data[y]; data[y] = x;
        }
        if(x != y) cnt--;
        return x != y;
    }
    // 判定
    bool ask(int x, int y) {
        return root(x) == root(y);
    }
    // 根
    int root(int x) {
        return data[x] < 0 ? x : data[x] = root(data[x]);
    }
    // xが属する集合の位数
    int size(int x) {
        return -data[root(x)];
    }
    // 集合の数
    int size() {
        return cnt;
    }
};

pair<Weight, Edges> kruskal(Graph const& g){
    int n = g.size();
    UnionFind uf(n+1);
    Edges es;
    rep(u, n) rep(i,g[u].size()) if (u < g[u][i].dst) es.push_back(g[u][i]);
    sort(all(es)); // !! INVERSE !!
    reverse(all(es));
    Weight total = 0;
    Edges res;
    for(auto const & e : es){
        if(!uf.ask(e.src,e.dst)){
            res.push_back(e);
            total += e.weight;
            uf.set(e.src,e.dst);
        }
    }
    return make_pair(total,res);
}

int main(){
    int n,m;
    while(cin>>n>>m && n){
        Graph g(n+1);
        rep(i,m){
            int a,b,c; cin >> a >> b >> c;
            g[a].eb(a,b,c); g[b].eb(b,a,c);
        }
        auto res = kruskal(g).second;
        cout << res[n/2-1].weight << endl;
    }
}
```