#include <bits/stdc++.h>
#define INFTY 1000001
#define MAX 1001
using namespace std;

class Edge{
public:
    int target, cost;
    Edge(int target = 0, int cost = 0) : target(target), cost(cost) {}
};

bool visited[MAX];
int parent[MAX], key[MAX];
int V, minv, min_index;

int minKey() {
    minv = INFTY;
    for (int v = 0; v < V; v++)
        if (!visited[v] && key[v] < minv)
            minv= key[v], min_index = v;
    return min_index;
}

void printMST()
{
    std::sort(key, key+V);
    int mid = V /2;
    printf("%d\n", key[mid]);
}

void prim(vector<Edge> G[]) {
    for (int i = 0; i < V; i++) {
        key[i] = INFTY;
        visited[i] = false;
        parent[i] = -1;
    }
    key[0] = 0;
    parent[0] = -1;

    int current, target, cost;

    for (int i = 0; i < V-1; i++) {
        current = minKey();
        visited[current] = true;

        for (unsigned long v = 0; v < G[current].size(); v++) {
            target = G[current][v].target;
            cost = G[current][v].cost;
            if (!visited[target] && cost < key[target])
                parent[target] = current, key[target] = cost;
        }
    }
    printMST();
}

int main()
{
    int E, source, cost, target;
    for (; ;) {
        std::scanf("%d %d", &V, &E);
        vector<Edge> G[V];
        if (V == 0 && E == 0) break;
        for (int i = 0; i < E; i++) {
            std::scanf("%d %d %d", &source, &target, &cost);
            G[--source].push_back(Edge(--target, cost));
            G[target].push_back(Edge(source, cost));
        }
        prim(G);
    }
    return 0;
}


### Prompt

Develop a solution in CPP to the problem described below:

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 INFTY 1000001
#define MAX 1001
using namespace std;

class Edge{
public:
    int target, cost;
    Edge(int target = 0, int cost = 0) : target(target), cost(cost) {}
};

bool visited[MAX];
int parent[MAX], key[MAX];
int V, minv, min_index;

int minKey() {
    minv = INFTY;
    for (int v = 0; v < V; v++)
        if (!visited[v] && key[v] < minv)
            minv= key[v], min_index = v;
    return min_index;
}

void printMST()
{
    std::sort(key, key+V);
    int mid = V /2;
    printf("%d\n", key[mid]);
}

void prim(vector<Edge> G[]) {
    for (int i = 0; i < V; i++) {
        key[i] = INFTY;
        visited[i] = false;
        parent[i] = -1;
    }
    key[0] = 0;
    parent[0] = -1;

    int current, target, cost;

    for (int i = 0; i < V-1; i++) {
        current = minKey();
        visited[current] = true;

        for (unsigned long v = 0; v < G[current].size(); v++) {
            target = G[current][v].target;
            cost = G[current][v].cost;
            if (!visited[target] && cost < key[target])
                parent[target] = current, key[target] = cost;
        }
    }
    printMST();
}

int main()
{
    int E, source, cost, target;
    for (; ;) {
        std::scanf("%d %d", &V, &E);
        vector<Edge> G[V];
        if (V == 0 && E == 0) break;
        for (int i = 0; i < E; i++) {
            std::scanf("%d %d %d", &source, &target, &cost);
            G[--source].push_back(Edge(--target, cost));
            G[target].push_back(Edge(source, cost));
        }
        prim(G);
    }
    return 0;
}


```