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 <bits/stdc++.h> // PLEASE

using namespace std;
typedef long long ll;
typedef pair <int, int> pp;
#define MAXN 1000005
#define MAXC 205
#define MAXP 25
#define A first
#define B second
#define MP make_pair
#define PB push_back
const ll INF = 2e9+13;
const ll MOD = 1e9+7;
int par[MAXN];
vector <int> adj[MAXN];
ll wt[MAXN];

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

void join(int x, int y)
{
	x = get(x); y = get(y);
	if(x == y) return;
	par[x] = y;
}

vector <ll> edg[MAXN];
int main(void)
{
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	int N, M;
	cin >> N >> M;
	for(int i=0; i<N; i++) cin >> wt[i];
	for(int i=0; i<N; i++) par[i] = i;
	for(int i=0; i<M; i++) {
		int a, b;
		cin >> a >> b;
		join(a, b);	
	}
	int cc = 0;
	bool is[MAXN];
	vector <int> v;
	for(int i=0; i<N; i++) {
		int x = get(i);
		if(!is[x]) {
			cc++;
			is[x] = 1;
			v.PB(x);
		}
	}
	int need = 2*(cc-1);
	if(need > N) {
		cout << "Impossible" << endl;
		return 0;
	}
	if(need <= 0) {
		cout << 0 << endl;
		return 0;
	}
	ll ans = 0;
	for(int i=0; i<N; i++) edg[get(i)].PB(wt[i]);
	for(int i=0; i<v.size(); i++) sort(edg[v[i]].begin(), edg[v[i]].end());
	for(int i=0; i<v.size(); i++) ans += edg[v[i]][0];
	need -= cc;
	vector <ll> oth;
	for(int i=0; i<v.size(); i++) {
		int u = v[i];
		for(int j=1; j<edg[u].size(); j++) oth.PB(edg[u][j]);
	}
	sort(oth.begin(), oth.end());
	for(int i=0; i<need; i++) ans += oth[i];
	cout << ans << endl;
}