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)

#define _CRT_SECURE_NO_WARNINGS

#include <vector>
#include <iostream>
#include <string>
#include <functional>
#include <set>
#include <map>
#include <unordered_map>
#include <fstream>
#include <iomanip>
#include <ctime>
#include <queue>
#include <deque>
#include <math.h>
#include <cmath>
#include <stack>
#include <algorithm>
#include <list>
#include <array>
#include <valarray>
#include <unordered_map>
#include <cassert>
#include <random>
#include <cstring>
#include <sstream>

using namespace std;

typedef long long li;
typedef pair<int, int> pii;

#define X first
#define Y second
#define all(a) a.begin(), a.end()
#define forn(i, n) for (int i = 0; i < (int)(n); ++i)

double eps = 1e-5;
const int INF = 2e9 + 7;
const li LINF = 9e18 + 7;

const int N = 1e5 + 7;

vector<int> g[N];
set<pair<li, int>> s[N];
set<pair<li, int>> comps;
int p[N];
li a[N];
bool used[N];
li ans;

int find(int v) {
	return v == p[v] ? v : p[v] = find(p[v]);
}

void merge(int u, int v) {
	u = find(u);
	v = find(v);

	if (s[u].empty() || s[v].empty()) {
		cout << "Impossible" << endl;
		exit(0);
	}

	if (s[u].size() < s[v].size())
		swap(u, v);

	p[v] = u;

	s[u].erase(s[u].begin());
	s[v].erase(s[v].begin());

	s[u].insert(all(s[v]));
	s[v].clear();

	if (s[u].empty() && comps.size()) {
		cout << "Impossible" << endl;
		exit(0);
	}

	comps.insert(*s[u].begin());
}

void dfs(int u, int root) {
	used[u] = true;
	s[root].insert({ a[u], u });
	p[u] = root;

	for (int v : g[u]) {
		if (!used[v])
			dfs(v, root);
	}
}

int main() {
#ifdef _DEBUG
	freopen("in.txt", "r", stdin);
	freopen("out.txt", "w", stdout);
#endif

	int n, m;
	cin >> n >> m;

	forn(i, n) {
		cin >> a[i];
	}

	forn(i, m) {
		int x, y;
		cin >> x >> y;

		g[x].push_back(y);
		g[y].push_back(x);
	}

	int cnt = 0;
	forn(i, n) {
		if (!used[i]) {
			dfs(i, i);
			comps.insert(*s[i].begin());
			cnt++;
		}
	}

	while (comps.size() > 1) {
		int u = comps.begin()->second;
		comps.erase(comps.begin());

		int v = comps.begin()->second;
		comps.erase(comps.begin());

		ans += a[u] + a[v];
		merge(u, v);
	}


	cout << ans << endl;
}