#include"bits/stdc++.h"
using namespace std;
typedef long long ll;
// run : ctrl + c 

template<class T>bool chmax(T &a,T b){if(a<b){a=b;return 1;} return 0;}
template<class T>bool chmin(T &a,T b){if(b<a){a=b;return 1;} return 0;}

// struct UnionFind{
//     vector<int> par;
//     Unionfind(int n){
//         par = vector<int>(n,-1);
//     }
//     int root(int a){
//         if(par[a]<0) return a;
//         return par[a] = root(par[a]);
//     }
//     int size(int a){
//         a = root(a);
//         return -par[a];
//     }
//     bool unite(int a,int b){
//         a = root(a);
//         b = root(b);
//         if(a==b) return false;

//         if(par[b] < par[a]){
//             swap(a,b);
//         }
//         par[a] += par[b];
//         par[b] = a;
//         return true;
//     }
//     bool same(int a,int b){
//         a = root(a);
//         b = root(b);
//         return (a == b);
//     }
// };

class UnionFind{
    public:
    //親の番号を格納する。親だった場合は-(その集合のサイズ)
    vector<int> parent;

    UnionFind(int N){
        parent = vector<int>(N,-1);
    }

    int root(int A){
        if(parent[A] < 0) return A;
        return parent[A]=root(parent[A]);
    }

    int size(int A){
        return -parent[root(A)];
    }

    bool unite(int A, int B) {
        A = root(A), B = root(B);
        if(A == B) return false; 

        if(size(A) < size(B)) swap(A,B);
        parent[A] += parent[B];
        parent[B] = A;
        return true;
    }

    bool same(int A, int B){
        return root(A)==root(B);
    } 
};


signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(20);

    
    int n,m;
    while(cin>>n>>m){
        if(n==0) return 0;
        array<int,3> d[m];
        for(int i=0;i<m;i++){
            int x,y,c;
            cin>>x>>y>>c;
            x--,y--;
            d[i] = {c,x,y};
        }
        sort(d,d+m);
        int cnt = 0;
        UnionFind uni(n);
        for(int i=0;i<m;i++){
            if(uni.same(d[i][1],d[i][2])) continue;
            cnt++;
uni.unite(d[i][1],d[i][2]);
            if(cnt == n/2){
                cout << d[i][0] << endl;
                break;
            }
        }

    }

}


### 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;
typedef long long ll;
// run : ctrl + c 

template<class T>bool chmax(T &a,T b){if(a<b){a=b;return 1;} return 0;}
template<class T>bool chmin(T &a,T b){if(b<a){a=b;return 1;} return 0;}

// struct UnionFind{
//     vector<int> par;
//     Unionfind(int n){
//         par = vector<int>(n,-1);
//     }
//     int root(int a){
//         if(par[a]<0) return a;
//         return par[a] = root(par[a]);
//     }
//     int size(int a){
//         a = root(a);
//         return -par[a];
//     }
//     bool unite(int a,int b){
//         a = root(a);
//         b = root(b);
//         if(a==b) return false;

//         if(par[b] < par[a]){
//             swap(a,b);
//         }
//         par[a] += par[b];
//         par[b] = a;
//         return true;
//     }
//     bool same(int a,int b){
//         a = root(a);
//         b = root(b);
//         return (a == b);
//     }
// };

class UnionFind{
    public:
    //親の番号を格納する。親だった場合は-(その集合のサイズ)
    vector<int> parent;

    UnionFind(int N){
        parent = vector<int>(N,-1);
    }

    int root(int A){
        if(parent[A] < 0) return A;
        return parent[A]=root(parent[A]);
    }

    int size(int A){
        return -parent[root(A)];
    }

    bool unite(int A, int B) {
        A = root(A), B = root(B);
        if(A == B) return false; 

        if(size(A) < size(B)) swap(A,B);
        parent[A] += parent[B];
        parent[B] = A;
        return true;
    }

    bool same(int A, int B){
        return root(A)==root(B);
    } 
};


signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(20);

    
    int n,m;
    while(cin>>n>>m){
        if(n==0) return 0;
        array<int,3> d[m];
        for(int i=0;i<m;i++){
            int x,y,c;
            cin>>x>>y>>c;
            x--,y--;
            d[i] = {c,x,y};
        }
        sort(d,d+m);
        int cnt = 0;
        UnionFind uni(n);
        for(int i=0;i<m;i++){
            if(uni.same(d[i][1],d[i][2])) continue;
            cnt++;
uni.unite(d[i][1],d[i][2]);
            if(cnt == n/2){
                cout << d[i][0] << endl;
                break;
            }
        }

    }

}


```