#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define all(a)  (a).begin(),(a).end()
#define vi vector<int>
#define pb push_back
#define INF 999999999
//#define INF (1LL<<59)
 
class UF{
private:
    vector<int> par,rank,elm;
public:
    int groups;
    
    UF(int __size):par(__size) , rank(__size,0) , elm(__size,1) , groups(__size){
        for(int i=0;i<__size;i++)par[i]=i;
    }
    
    int elements(int n){
        return elm[find(n)];
    }
    
    int find(int x){
        if(par[x]==x) {
            return x;
        }else{
            return par[x]=find(par[x]);
        }
    }
    
    void unite(int x,int y){
        x=find(x);
        y=find(y);
        if(x==y) return;
        
        groups--;
        if(rank[x]<rank[y]){
            par[x]=y;
            elm[y]+=elm[x];
        }else{
            par[y]=x;
            elm[x]+=elm[y];
            if(rank[x]==rank[y])rank[x]++;
        }
    }
    
    bool isSame(int x,int y){
        return find(x)==find(y);
    }
};
 
#define MAX_N 1000
struct edge{int to,cost;};
vector<edge> G[MAX_N];
int kraskal(int n,vector<int> &list){
    int ret = 0;
    vector< pair< int,pii > > edges;
    
    rep(i,MAX_N){
        rep(j,G[i].size()){
            edges.pb( make_pair(G[i][j].cost,make_pair(i,G[i][j].to)) );
        }
    }
    
    sort(all(edges));
    
    UF uf(n);
    
    rep(i,edges.size()){
        pii e = edges[i].second;
        
        if(!uf.isSame(e.first,e.second)){
            uf.unite(e.first,e.second);
            ret+=edges[i].first;
            list.pb(edges[i].first);
        }
    }
    return ret;
}
 
 
 
int main(){
    int n,m;
    while(cin>>n>>m&&(n||m)){
        rep(i,MAX_N)G[i].clear();
        rep(i,m){
            int s,t,c;
            cin>>s>>t>>c;
            s--,t--;
            G[s].pb(edge{t,c});
            G[t].pb(edge{s,c});
        }
        vector<int> list;
        kraskal(n,list);
        sort(all(list));
        cout<<list[list.size()/2]<<endl;
    }
}
### 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;
typedef long long ll;
typedef pair<int,int> pii;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define all(a)  (a).begin(),(a).end()
#define vi vector<int>
#define pb push_back
#define INF 999999999
//#define INF (1LL<<59)
 
class UF{
private:
    vector<int> par,rank,elm;
public:
    int groups;
    
    UF(int __size):par(__size) , rank(__size,0) , elm(__size,1) , groups(__size){
        for(int i=0;i<__size;i++)par[i]=i;
    }
    
    int elements(int n){
        return elm[find(n)];
    }
    
    int find(int x){
        if(par[x]==x) {
            return x;
        }else{
            return par[x]=find(par[x]);
        }
    }
    
    void unite(int x,int y){
        x=find(x);
        y=find(y);
        if(x==y) return;
        
        groups--;
        if(rank[x]<rank[y]){
            par[x]=y;
            elm[y]+=elm[x];
        }else{
            par[y]=x;
            elm[x]+=elm[y];
            if(rank[x]==rank[y])rank[x]++;
        }
    }
    
    bool isSame(int x,int y){
        return find(x)==find(y);
    }
};
 
#define MAX_N 1000
struct edge{int to,cost;};
vector<edge> G[MAX_N];
int kraskal(int n,vector<int> &list){
    int ret = 0;
    vector< pair< int,pii > > edges;
    
    rep(i,MAX_N){
        rep(j,G[i].size()){
            edges.pb( make_pair(G[i][j].cost,make_pair(i,G[i][j].to)) );
        }
    }
    
    sort(all(edges));
    
    UF uf(n);
    
    rep(i,edges.size()){
        pii e = edges[i].second;
        
        if(!uf.isSame(e.first,e.second)){
            uf.unite(e.first,e.second);
            ret+=edges[i].first;
            list.pb(edges[i].first);
        }
    }
    return ret;
}
 
 
 
int main(){
    int n,m;
    while(cin>>n>>m&&(n||m)){
        rep(i,MAX_N)G[i].clear();
        rep(i,m){
            int s,t,c;
            cin>>s>>t>>c;
            s--,t--;
            G[s].pb(edge{t,c});
            G[t].pb(edge{s,c});
        }
        vector<int> list;
        kraskal(n,list);
        sort(all(list));
        cout<<list[list.size()/2]<<endl;
    }
}
```