#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
const int INF = 1e9;
const ll LINF = 1e18;

struct UF{
    vector<ll> d;
    UF(ll size):d(size,-1){}
    void init(){
        fill(d.begin(),d.end(),-1);
    }
    bool u(ll x,ll y){
        x = r(x); y = r(y);
        if(x != y){
            if(d[y] < d[x]) swap(x,y);
            d[x] += d[y]; d[y] = x;
        }
        return x!=y;
    }
    bool f(ll x,ll y){
        return r(x) == r(y);
    }
    ll r(ll x){
        return d[x] < 0 ? x:d[x] = r(d[x]);
    }
    ll s(ll x){
        return -d[r(x)];
    }
};

ll n,m;
struct edge{
    ll u,v,cost;
    edge(){}
    edge(ll u,ll v,ll cost):u(u),v(v),cost(cost){}
    bool operator < (const edge& e) const{
        return cost < e.cost;
    }    bool operator > (const edge& e) const{
        return cost > e.cost;
    }
};
ll solve(){
    ll res = LINF;
    vector<ll> s(m),t(m),c(m);
    vector<edge> edges(m);
    for(int i = 0; i < m;i++){
        ll s,t,c; cin >> s >> t >> c; s--; t--;
        edges[i] = edge(s,t,c);
    }
    sort(edges.begin(),edges.end());
    UF uf(n);
    vector<int> f(m);
    vector<ll> C;
    for(int i = 0; i < m;i++){
        if(uf.f(edges[i].u,edges[i].v)) continue;
        f[i] = true;
        uf.u(edges[i].u,edges[i].v);
        C.push_back(edges[i].cost);
    }
    sort(C.begin(),C.end());
    res = C[(n-1)/2];
//    for(int i = 0; i < m;i++){
//        if(edges[i].cost > res) break;
//        if(f[i]) continue;
//        C.clear();
//        uf.init();
//        C.push_back(edges[i].cost);
//        uf.u(edges[i].u,edges[i].v);
//        for(int j = 0; j < m;j++){
//            if(i == j) continue;
//            if(uf.f(edges[j].u,edges[j].v)) continue;
//            uf.u(edges[j].u,edges[j].v);
//            C.push_back(edges[j].cost);
//        }
//        if(uf.s(0) != n) continue;
//        sort(C.begin(),C.end());
//        res = min(res,C[(n-1)/2]);
//    }
    return res;
}
int main(void){
    cin.tie(0); ios_base::sync_with_stdio(false);
    while(cin >> n >> m,n|m){
        cout << solve() << endl;
    }
    return 0;
}


### 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
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
const int INF = 1e9;
const ll LINF = 1e18;

struct UF{
    vector<ll> d;
    UF(ll size):d(size,-1){}
    void init(){
        fill(d.begin(),d.end(),-1);
    }
    bool u(ll x,ll y){
        x = r(x); y = r(y);
        if(x != y){
            if(d[y] < d[x]) swap(x,y);
            d[x] += d[y]; d[y] = x;
        }
        return x!=y;
    }
    bool f(ll x,ll y){
        return r(x) == r(y);
    }
    ll r(ll x){
        return d[x] < 0 ? x:d[x] = r(d[x]);
    }
    ll s(ll x){
        return -d[r(x)];
    }
};

ll n,m;
struct edge{
    ll u,v,cost;
    edge(){}
    edge(ll u,ll v,ll cost):u(u),v(v),cost(cost){}
    bool operator < (const edge& e) const{
        return cost < e.cost;
    }    bool operator > (const edge& e) const{
        return cost > e.cost;
    }
};
ll solve(){
    ll res = LINF;
    vector<ll> s(m),t(m),c(m);
    vector<edge> edges(m);
    for(int i = 0; i < m;i++){
        ll s,t,c; cin >> s >> t >> c; s--; t--;
        edges[i] = edge(s,t,c);
    }
    sort(edges.begin(),edges.end());
    UF uf(n);
    vector<int> f(m);
    vector<ll> C;
    for(int i = 0; i < m;i++){
        if(uf.f(edges[i].u,edges[i].v)) continue;
        f[i] = true;
        uf.u(edges[i].u,edges[i].v);
        C.push_back(edges[i].cost);
    }
    sort(C.begin(),C.end());
    res = C[(n-1)/2];
//    for(int i = 0; i < m;i++){
//        if(edges[i].cost > res) break;
//        if(f[i]) continue;
//        C.clear();
//        uf.init();
//        C.push_back(edges[i].cost);
//        uf.u(edges[i].u,edges[i].v);
//        for(int j = 0; j < m;j++){
//            if(i == j) continue;
//            if(uf.f(edges[j].u,edges[j].v)) continue;
//            uf.u(edges[j].u,edges[j].v);
//            C.push_back(edges[j].cost);
//        }
//        if(uf.s(0) != n) continue;
//        sort(C.begin(),C.end());
//        res = min(res,C[(n-1)/2]);
//    }
    return res;
}
int main(void){
    cin.tie(0); ios_base::sync_with_stdio(false);
    while(cin >> n >> m,n|m){
        cout << solve() << endl;
    }
    return 0;
}


```