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)

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <set>
#include <queue>
#include <deque>
#include <map>
#include <stack>
#include<bitset>
#include<list>
#include<cassert>
#include<numeric>
 
 
using namespace std;

const int N = 100 * 1000;
int value[N];
int mark[N];
vector<int> graph[N];
multiset<int> comp[N];
int ans = 0;
int one = 0;
int other = 0;
int sz = 0;
int n, m, mh;
void input()
{
	cin >> n >> m;
	for (int i = 0 ; i < n; i++)
	{
		cin >> value[i];
	}
	for (int i = 0; i < m; i++)
	{
		int u, v;
		cin >> u >> v;
		graph[u].push_back(v);
		graph[v].push_back(u);
	}
}
void dfs(int v)
{
	comp[mh].insert(value[v]);
	mark[v] = true;
	for (int i = 0; i < graph[v].size(); i++)
	{
		int u = graph[v][i];
		if (!mark[u])
		{
			dfs(u);
		}
	}
	sz++;
	if (sz == 1)
		one++;
	else
		other += sz;
}
int main()
{
	input();
	for (int i = 0; i < n; i++)
	{
		if (!mark[i])
		{
			sz = 0;
			dfs(i);
			mh++;
		}
	}
	if (mh == 1)
	{
		cout << 0;
		exit(0);
	}
	if (one == 2 && other == 0)
	{
		cout << value[0] + value[1];
		exit(0);
	}
	if (one > other)
	{
		cout << "Impossible";
		exit(0);
	}
	vector<int> tmp;
	for (int i = 0; i < mh; i++)
	{
		ans += *(comp[i].begin());
		comp[i].erase(*comp[i].begin());
		for (auto nei: comp[i])
		{
			tmp.push_back(nei);
		}
	}
	sort(tmp.begin(), tmp.end());
	for (int i = 0; i < mh - 2; i++)
	{
		ans += tmp[i];
	}

	cout << ans << endl;



}