#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)n;++i)
#define all(v) (v).begin(),(v).end()

using namespace std;

typedef pair<int,int>P;

struct edge{
    int u;	//?????????
    int v;	//??°??????
    int cost;	//??????
    //???????????????????????§?????§?°???¢????????????
    bool operator<(const edge& another) const {
        return cost < another.cost;
    }
};

const int MAX_N = 1002;
const int MAX_M = 10002;

int n,m;
edge es[MAX_M];
int par[MAX_N];
int rrank[MAX_N];

void initial(int n){		//?????????
	rep(i,n){
		par[i] = i;
		rrank[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???????????¨??¨y???????????¨?????????
	x = find(x);	//x???????????¨??????????????????x??¨??????
	y = find(y);	//y???????????¨??????????????????y??¨??????
	if(x == y) return;
	if(rrank[x] < rrank[y]){
		par[x] = y;
	}else{
		par[y] = x;
		if(rrank[x] == rrank[y])
			rrank[x]++;
	}
}

bool same(int x,int y){	//x,y???????????¨???????????§?????????
	return find(x) == find(y);
}

P kruskal(int n,int m){
    vector<int> vec;
	initial(n);
	int res = 0;
	rep(i,m){
		edge e = es[i];
		if(!same(e.u,e.v)){
			unite(e.u,e.v);
            vec.push_back(e.cost);
			res += e.cost;
		}
	}
    if(vec.size() % 2 == 0){
        int hoge = vec.size() / 2 - 1;
        int sm = vec[hoge] + vec[hoge+1];
        if(sm % 2 == 0){
            return P(sm/2,0);
        }else{
            return P(sm/2,1);
        }
    }else{
        return P(vec[(vec.size()-1)/2],0);
    }
}

int main()
{
    while(1){
        scanf("%d%d",&n,&m);
        if(n == 0){
            break;
        }
        rep(i,m){
            int p,q,r;
            scanf("%d%d%d",&p,&q,&r);
            es[i] = (edge){p-1,q-1,r};
        }
        sort(es,es+m);
        P p = kruskal(n,m);
        if(p.second == 0){
            cout << p.first << "\n";
        }else{
            cout << p.first + 0.5 << "\n";
        }
    }
    return 0;
}
### 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>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)n;++i)
#define all(v) (v).begin(),(v).end()

using namespace std;

typedef pair<int,int>P;

struct edge{
    int u;	//?????????
    int v;	//??°??????
    int cost;	//??????
    //???????????????????????§?????§?°???¢????????????
    bool operator<(const edge& another) const {
        return cost < another.cost;
    }
};

const int MAX_N = 1002;
const int MAX_M = 10002;

int n,m;
edge es[MAX_M];
int par[MAX_N];
int rrank[MAX_N];

void initial(int n){		//?????????
	rep(i,n){
		par[i] = i;
		rrank[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???????????¨??¨y???????????¨?????????
	x = find(x);	//x???????????¨??????????????????x??¨??????
	y = find(y);	//y???????????¨??????????????????y??¨??????
	if(x == y) return;
	if(rrank[x] < rrank[y]){
		par[x] = y;
	}else{
		par[y] = x;
		if(rrank[x] == rrank[y])
			rrank[x]++;
	}
}

bool same(int x,int y){	//x,y???????????¨???????????§?????????
	return find(x) == find(y);
}

P kruskal(int n,int m){
    vector<int> vec;
	initial(n);
	int res = 0;
	rep(i,m){
		edge e = es[i];
		if(!same(e.u,e.v)){
			unite(e.u,e.v);
            vec.push_back(e.cost);
			res += e.cost;
		}
	}
    if(vec.size() % 2 == 0){
        int hoge = vec.size() / 2 - 1;
        int sm = vec[hoge] + vec[hoge+1];
        if(sm % 2 == 0){
            return P(sm/2,0);
        }else{
            return P(sm/2,1);
        }
    }else{
        return P(vec[(vec.size()-1)/2],0);
    }
}

int main()
{
    while(1){
        scanf("%d%d",&n,&m);
        if(n == 0){
            break;
        }
        rep(i,m){
            int p,q,r;
            scanf("%d%d%d",&p,&q,&r);
            es[i] = (edge){p-1,q-1,r};
        }
        sort(es,es+m);
        P p = kruskal(n,m);
        if(p.second == 0){
            cout << p.first << "\n";
        }else{
            cout << p.first + 0.5 << "\n";
        }
    }
    return 0;
}
```