#include<bits/stdc++.h>
using namespace std;
#define fs first
#define sc second
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define ALL(A) A.begin(),A.end()
#define RALL(A) A.rbegin(),A.rend()
typedef long long LL;
typedef pair<int,int> P;
const LL mod=998244353;
const LL LINF=1LL<<62;
const int INF=1<<20;


const int M_N=200001;

struct UnionFind{
    int par[M_N];
    int rank[M_N];

    void init(int n){
        for(int i=0;i<n;i++){
            par[i]=i;
            rank[i]=0;
        }
    }

    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;
        if(rank[x]<rank[y]){
            par[x]=y;
        }
        else{
            par[y]=x;
            if(rank[x]==rank[y]) rank[x]++;
        }
    }

    bool same(int x,int y){
        return find(x)==find(y);
    }
};

struct edge { int from;int to;int cost;};

int main(){
    int n,m;
    while(cin >> n >> m){
        if(!n&&!m) break;
        UnionFind uf; 
        uf.init(n+1);
        vector<edge> v;
        for (int i = 0; i < m; i++) {
            int x,y,c;cin >> x >> y >> c;
            v.pb({x,y,c});
        }
        sort(ALL(v),[](const edge &right ,const edge &left){ return right.cost<left.cost;});
        int k=0;
        for (int i = 0; i < m; i++) {
            edge e=v[i];
            if(uf.same(e.from,e.to)) continue;
            uf.unite(e.from,e.to);
            k++;
            if(k==n/2){
                cout << e.cost << endl;
                break;
            }
        }
    }
    return 0;
}



### Prompt

Your task is to create 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 fs first
#define sc second
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define ALL(A) A.begin(),A.end()
#define RALL(A) A.rbegin(),A.rend()
typedef long long LL;
typedef pair<int,int> P;
const LL mod=998244353;
const LL LINF=1LL<<62;
const int INF=1<<20;


const int M_N=200001;

struct UnionFind{
    int par[M_N];
    int rank[M_N];

    void init(int n){
        for(int i=0;i<n;i++){
            par[i]=i;
            rank[i]=0;
        }
    }

    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;
        if(rank[x]<rank[y]){
            par[x]=y;
        }
        else{
            par[y]=x;
            if(rank[x]==rank[y]) rank[x]++;
        }
    }

    bool same(int x,int y){
        return find(x)==find(y);
    }
};

struct edge { int from;int to;int cost;};

int main(){
    int n,m;
    while(cin >> n >> m){
        if(!n&&!m) break;
        UnionFind uf; 
        uf.init(n+1);
        vector<edge> v;
        for (int i = 0; i < m; i++) {
            int x,y,c;cin >> x >> y >> c;
            v.pb({x,y,c});
        }
        sort(ALL(v),[](const edge &right ,const edge &left){ return right.cost<left.cost;});
        int k=0;
        for (int i = 0; i < m; i++) {
            edge e=v[i];
            if(uf.same(e.from,e.to)) continue;
            uf.unite(e.from,e.to);
            k++;
            if(k==n/2){
                cout << e.cost << endl;
                break;
            }
        }
    }
    return 0;
}



```