#include <bits/stdc++.h>
#define For(i, a, b) for(int (i)=(int)(a); (i)<(int)(b); ++(i))
#define rFor(i, a, b) for(int (i)=(int)(a)-1; (i)>=(int)(b); --(i))
#define rep(i, n) For(i, 0, n)
#define rrep(i, n) rFor(i, n, 0)
#define fi first
#define se second
using namespace std;
typedef long long lint;
typedef unsigned long long ulint;
typedef pair<int, int> pii;
typedef pair<lint, lint> pll;
template<class T> bool chmax(T &a, const T &b){if(a<b){a=b; return true;} return false;}
template<class T> bool chmin(T &a, const T &b){if(a>b){a=b; return true;} return false;}
template<class T> T div_floor(T a, T b){
    if(b < 0) a *= -1, b *= -1;
    return a>=0 ? a/b : (a+1)/b-1;
}
template<class T> T div_ceil(T a, T b){
    if(b < 0) a *= -1, b *= -1;
    return a>0 ? (a-1)/b+1 : a/b;
}

constexpr lint mod = 1000000007;
constexpr lint INF = mod * mod;
constexpr int MAX = 200010;

typedef struct UnionFindTree{
    vector<int> par;

    UnionFindTree(int n){
        par.resize(n, -1);
    }

    bool is_root(int x){
        return par[x]<0;
    }

    int find(int x){
        if(is_root(x)) return x;
        return par[x] = find(par[x]);
    }

    int size(int x){
        return -par[find(x)];
    }

    bool unite(int x, int y){
        x = find(x);
        y = find(y);
        if(x == y) return false;
        if(size(x) < size(y)) swap(x, y);
        par[x] += par[y];
        par[y] = x;
        return true;
    }

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

template<typename T> struct edge{
    int from, to; T cost;
    edge(int f, int t, T c): from(f), to(t), cost(c){}
};
 
template<typename T> struct Graph{
    vector<vector<edge<T>>> G;
    int n;
 
    Graph(int n_): n(n_){
        G.resize(n);
    }
 
    void add_edge(int f, int t, T c){
        G[f].emplace_back(f, t, c);
    }
};

int n, m;

void solve(){
    vector<edge<int>> E;
    rep(i, m){
        int a, b, c;
        scanf("%d%d%d", &a, &b, &c);
        --a; --b;
        E.emplace_back(a, b, c);
    }
    UF uf(n);
    sort(E.begin(), E.end(), [](const edge<int> &e1, const edge<int> &e2){
        return e1.cost < e2.cost;
    });
    vector<int> mst;
    for(auto &e: E){
        if(uf.unite(e.from, e.to)) mst.push_back(e.cost);
    }
    printf("%d\n", mst[n / 2 - 1]);
}

int main(){
    while(scanf("%d%d", &n, &m) && n){
        solve();
    }
}

### Prompt

Please create a solution in Cpp 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>
#define For(i, a, b) for(int (i)=(int)(a); (i)<(int)(b); ++(i))
#define rFor(i, a, b) for(int (i)=(int)(a)-1; (i)>=(int)(b); --(i))
#define rep(i, n) For(i, 0, n)
#define rrep(i, n) rFor(i, n, 0)
#define fi first
#define se second
using namespace std;
typedef long long lint;
typedef unsigned long long ulint;
typedef pair<int, int> pii;
typedef pair<lint, lint> pll;
template<class T> bool chmax(T &a, const T &b){if(a<b){a=b; return true;} return false;}
template<class T> bool chmin(T &a, const T &b){if(a>b){a=b; return true;} return false;}
template<class T> T div_floor(T a, T b){
    if(b < 0) a *= -1, b *= -1;
    return a>=0 ? a/b : (a+1)/b-1;
}
template<class T> T div_ceil(T a, T b){
    if(b < 0) a *= -1, b *= -1;
    return a>0 ? (a-1)/b+1 : a/b;
}

constexpr lint mod = 1000000007;
constexpr lint INF = mod * mod;
constexpr int MAX = 200010;

typedef struct UnionFindTree{
    vector<int> par;

    UnionFindTree(int n){
        par.resize(n, -1);
    }

    bool is_root(int x){
        return par[x]<0;
    }

    int find(int x){
        if(is_root(x)) return x;
        return par[x] = find(par[x]);
    }

    int size(int x){
        return -par[find(x)];
    }

    bool unite(int x, int y){
        x = find(x);
        y = find(y);
        if(x == y) return false;
        if(size(x) < size(y)) swap(x, y);
        par[x] += par[y];
        par[y] = x;
        return true;
    }

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

template<typename T> struct edge{
    int from, to; T cost;
    edge(int f, int t, T c): from(f), to(t), cost(c){}
};
 
template<typename T> struct Graph{
    vector<vector<edge<T>>> G;
    int n;
 
    Graph(int n_): n(n_){
        G.resize(n);
    }
 
    void add_edge(int f, int t, T c){
        G[f].emplace_back(f, t, c);
    }
};

int n, m;

void solve(){
    vector<edge<int>> E;
    rep(i, m){
        int a, b, c;
        scanf("%d%d%d", &a, &b, &c);
        --a; --b;
        E.emplace_back(a, b, c);
    }
    UF uf(n);
    sort(E.begin(), E.end(), [](const edge<int> &e1, const edge<int> &e2){
        return e1.cost < e2.cost;
    });
    vector<int> mst;
    for(auto &e: E){
        if(uf.unite(e.from, e.to)) mst.push_back(e.cost);
    }
    printf("%d\n", mst[n / 2 - 1]);
}

int main(){
    while(scanf("%d%d", &n, &m) && n){
        solve();
    }
}

```