Problem:
Score : 600 points

Problem Statement

You are given a forest with N vertices and M edges. The vertices are numbered 0 through N-1.
The edges are given in the format (x_i,y_i), which means that Vertex x_i and y_i are connected by an edge.

Each vertex i has a value a_i.
You want to add edges in the given forest so that the forest becomes connected.
To add an edge, you choose two different vertices i and j, then span an edge between i and j.
This operation costs a_i + a_j dollars, and afterward neither Vertex i nor j can be selected again.

Find the minimum total cost required to make the forest connected, or print Impossible if it is impossible.

Constraints

1 ≤ N ≤ 100,000

0 ≤ M ≤ N-1

1 ≤ a_i ≤ 10^9

0 ≤ x_i,y_i ≤ N-1

The given graph is a forest.

All input values are integers.

Input

Input is given from Standard Input in the following format:

N M
a_0 a_1 .. a_{N-1}
x_1 y_1
x_2 y_2
:
x_M y_M

Output

Print the minimum total cost required to make the forest connected, or print Impossible if it is impossible.

Sample Input 1

7 5
1 2 3 4 5 6 7
3 0
4 0
1 2
1 3
5 6

Sample Output 1

7

If we connect vertices 0 and 5, the graph becomes connected, for the cost of 1 + 6 = 7 dollars.

Sample Input 2

5 0
3 1 4 1 5

Sample Output 2

Impossible

We can't make the graph connected.

Sample Input 3

1 0
5

Sample Output 3

0

The graph is already connected, so we do not need to add any edges.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

// All Heil Fire Lord Zuko

#include <bits/stdc++.h>
using namespace std;

#define all(x) x.begin(), x.end()

const int N = 100 * 1000 + 19;

int n, m, a[N];
vector<int> adj[N];
vector <long long> v, vec;
bool mark[N];

void dfs(int v);

int main() {
    ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
    cin >> n >> m;
    for (int i = 0; i < n; i ++)
        cin >> a[i];
    for (int i = 0; i < m; i ++) {
        int u, v;
        cin >> u >> v;
        adj[u].push_back(v);
        adj[v].push_back(u);
    }
    long long ans = 0, cnt = 0;
    if (m = n - 1)
        return cout << 0, 0;
    if (n < 2 * (n - m - 1))
        return cout << "Impossible", 0;
    for (int i = 0; i < n; i ++)
        if (!mark[i]) {
            vec.clear();
            dfs(i);
            sort(all(vec));
            ans += vec[0], cnt ++;
            for (int j = 1; j < (int)vec.size(); j ++)
                v.push_back(vec[j]);
        }
    sort(all(v));
    int i = 0;
    while (i < (int)v.size() && cnt < 2 * (n - m - 1)) {
        ans += v[i];
        cnt ++;
        i ++;
    }
    cout << ans;
    return 0;
}

void dfs(int v) {
    mark[v] = true;
    vec.push_back(a[v]);
    for (auto u : adj[v])
        if (!mark[u])
            dfs(u);
}

/* THINGS TO CHECK !! */

// Runtime ->
// Overflows ->
// Order is ->

/* READ PROBLEM STATEMENT CAREFULLY */