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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>

using namespace std;

typedef long long int ll;

const int N = 1e5 + 5;

vector < int > p (N), sz (N, 1);
vector < vector < int > > g (N);

int find (int u) {
  if (u == p[u]) return u;
  return p[u] = find (p[u]);
}

void merge (int u, int v) {
  u = find (u);
  v = find (v);
  if (u != v) {
    if (sz[u] > sz[v]) swap (u, v);
    p[u] = v;
    sz[v] += sz[u];
  }
}

int main () {
  ios_base::sync_with_stdio(false);
  cin.tie(0);cout.tie(0);

  int n, m;
  cin >> n >> m;
  vector < int > a (n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    p[i] = i;
  }

  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    merge (u, v);
  }

  for (int i = 0; i < n; i++) {
    g[find (i)].push_back(i);
  }

  vector < pair < ll, ll > > v;
  int cnt = 0;
  for (int i = 0; i < n; i++) {
    pair < ll, ll > p = {LLONG_MAX, LLONG_MAX};
    for (auto to : g[i]) {
      if (a[to] <= p.first) {
        p.second = p.first;
        p.first = a[to];
      } else if (a[to] < p.second) {
        p.second = a[to];
      }
    }
    if (g[i].size() == 0) continue;
    if (g[i].size() == 1) {
      cnt++;
      p.second = 1e17;
    }
    v.push_back(p);
  }

  if (cnt > 2) {
    cout << "Impossible\n";
  } else {
    sort (v.begin(), v.end(), [](const pair < ll, ll > lhs, const pair < ll, ll > rhs) -> bool{
            return lhs.second < rhs.second;
          });

    if (v.size() == 1) {
      cout << 0 << '\n';
      return 0;
    }

    ll ans = 0;
    for (int i = 0; i < v.size() - 2; i++) ans += v[i].first + v[i].second;
    ans += v.back().first;
    v.pop_back();
    ans += v.back().first;

    cout << ans << '\n';
  }
}