#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <string.h>

using namespace std;

const int MAXN = 200000 + 100;
int n, m;
struct Node
{
    int u, v, w;
}edge[MAXN];
int pre[MAXN];

int finds(int x)
{
    return x == pre[x] ? x : (pre[x] = finds(pre[x]));
}

bool cmp(Node a, Node b)
{
    return a.w < b.w;
}

void solve()
{
    int ans = 0;

    sort(edge, edge + m, cmp);

    for (int i = 0; i <= n; i++)
    {
        pre[i] = i;
    }

    int num = 0;

    for (int i = 0; i < m; i++)
    {
        int fa = finds(edge[i].u), fb = finds(edge[i].v);

        if (fa != fb)
        {
            pre[fa] = fb;
            num++;
            if (num == n / 2) ans = edge[i].w;
            if (num == n - 1) break;
        }
    }

    printf("%d\n", ans);
}

void input()
{
    int u, v, w;

    while (scanf("%d %d", &n, &m) != EOF)
    {
        if (n == 0 && m == 0)
        {
            break;
        }
        for (int i = 0; i < m; i++)
        {
            scanf("%d %d %d", &edge[i].u, &edge[i].v, &edge[i].w);
        }

        solve();
    }
}

int main()
{
    input();
    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 <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <string.h>

using namespace std;

const int MAXN = 200000 + 100;
int n, m;
struct Node
{
    int u, v, w;
}edge[MAXN];
int pre[MAXN];

int finds(int x)
{
    return x == pre[x] ? x : (pre[x] = finds(pre[x]));
}

bool cmp(Node a, Node b)
{
    return a.w < b.w;
}

void solve()
{
    int ans = 0;

    sort(edge, edge + m, cmp);

    for (int i = 0; i <= n; i++)
    {
        pre[i] = i;
    }

    int num = 0;

    for (int i = 0; i < m; i++)
    {
        int fa = finds(edge[i].u), fb = finds(edge[i].v);

        if (fa != fb)
        {
            pre[fa] = fb;
            num++;
            if (num == n / 2) ans = edge[i].w;
            if (num == n - 1) break;
        }
    }

    printf("%d\n", ans);
}

void input()
{
    int u, v, w;

    while (scanf("%d %d", &n, &m) != EOF)
    {
        if (n == 0 && m == 0)
        {
            break;
        }
        for (int i = 0; i < m; i++)
        {
            scanf("%d %d %d", &edge[i].u, &edge[i].v, &edge[i].w);
        }

        solve();
    }
}

int main()
{
    input();
    return 0;
}
```