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: Runtime Error)

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

typedef long long ll;
typedef pair<int, int> P;
typedef pair<ll, ll> LP;

#define pb push_back
#define rep(i, a, n) for(int i = (a); i < (n); i++)
#define dep(i, a, n) for(int i = (a); i >= (n); i--)
#define mod (ll)(1e9+7)
#define int ll

__attribute__((constructor))
void initial() {
  cin.tie(0);
  ios::sync_with_stdio(false);
}

int par[100001], ran[100001];

int find(int x) {
  if(par[x] == x) return x;
  else return par[x] = find(par[x]);
}

void unite(int x, int y) {
  x = find(x);
  y = find(y);
  if(x == y) return;
  if(ran[x] < ran[y]) {
    par[x] = y;
  }else {
    par[y] = x;
    if(ran[x] == ran[y]) ran[x]++;
  }
}

bool same(int x, int y) {
  return find(x) == find(y);
}

int s[100001], si[100001];

signed main() {
  int v, e, rc = 0;
  cin >> v >> e;
  for(int i = 0; i < v; i++) par[i] = i, ran[i] = 0;
  rep(i, 0, v) {
    cin >> s[i];
  }
  if((e + 1) * 2 < v) {
    cout << "Impossible" << endl;
    return 0;
  }
  rep(i, 0, e) {
    int a, b;
    cin >> a >> b;
    unite(a, b);
  }
  int ans = 0;
  while(1) {
    map<int, P> mp;
    map<int, vector<int> > mmp;
    rep(i, 0, v) find(i);
    rep(i, 0, v) {
      if(si[i]) continue;
      if(mp[par[i]].second) {
        if(mp[par[i]].second > s[i]) {
          mp[par[i]].second = s[i];
          mp[par[i]].first = i;
        }
      }
      else mp[par[i]] = P(i, s[i]);
      mmp[s[i]].pb(i);
    }
    if(mp.size() <= 1) break;
    for(auto it = mmp.begin(); it != mmp.end(); it++) {
      rep(i, 0, it->second.size()) {
        for(auto itr = mp.begin(); itr != mp.end(); itr++) {
          P c;
          c = itr->second;
          if(si[c.second] || si[it->second[i]]) continue;
          if(c.first == it->second[i] || same(c.first, it->second[i])) continue;
          unite(c.first, it->second[i]);
          si[c.first] = 1;
          si[it->second[i]] = 1;
          ans += it->first + c.second;
          break;
        }
      }
    }
  }
  cout << ans << endl;
}