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"
using namespace std;

#define DEBUG(x) cout<<#x<<": "<<x<<endl;
#define DEBUG_VEC(v) cout<<#v<<":";for(int i=0;i<v.size();i++) cout<<" "<<v[i]; cout<<endl

typedef long long ll;
#define int ll
#define vi vector<int>
#define vl vector<ll>
#define vii vector< vector<int> >
#define vll vector< vector<ll> >
#define vs vector<string>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define pll pair<ll,ll>
const int inf = 1000000001;
const ll INF = 2e18 * 2;
#define MOD 1000000007
#define mod 1000000009
#define pi 3.14159265358979323846
#define Sp(p) cout<<setprecision(15)<< fixed<<p<<endl;
int dx[4] = { 1,0,-1,0 }, dy[4] = { 0,1,0,-1 };
int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };



#define N 100010
#define R 100010
int n, m, r;
vector< pair<ll, pll> > M(R);
//vector<bool> used(N, false);
vl par(N);
vl ran(N);
vl num(N);
//vi a(N);

//n要素で初期化
void init(int n) {
	int i;
	for (i = 0; i < n; i++) {
		par[i] = i;
		ran[i] = 0;
		num[i] = 1;
	}
}

//木の根を求める
int find(int x) {
	if (par[x] == x) {
		return x;
	}
	else {
		return par[x] = find(par[x]);
	}
}

//xとyの属する集合を併合
void unite(int x, int y) {
	x = find(x);
	y = find(y);
	int numsum = num[x] + num[y];
	if (x == y) {
		return;
	}
	if (ran[x]<ran[y]) {
		par[x] = y;
	}
	else {
		par[y] = x;
		if (ran[x] == ran[y]) {
			ran[x]++;
		}
	}
	num[x] = num[y] = numsum;
}

//xとyが同じ集合に属するか否か
bool same(int x, int y) {
	return find(x) == find(y);
}


signed main() {
	int i, j;
	cin >> n >> m;
	vector<pii> a(n);
	for (i = 0; i < n; i++) {
		cin >> a[i].first;
		a[i].second = i;
	}
	sort(a.begin(), a.end());
	init(n);
	vi x(m), y(m);
	vector<bool> used(n, false);
	for (i = 0; i < m; i++) {
		cin >> x[i] >> y[i];
		unite(x[i], y[i]);
	}
	int cnt = 0;
	for (i = 0; i < n; i++) {
		int temp = find(i);
		if (!used[temp]) {
			used[temp] = true;
			cnt++;
		}
	}
	if (cnt == 1) {
		cout << 0 << endl;
		return 0;
	}

	priority_queue < pii, vector<pii>, greater<pii> > pq;
	for (i = 0; i < n; i++) {
		pq.push(a[i]);
	}
	pii now = pq.top();
	pq.pop();
	queue<pii> que;
	int ans = 0;
	while (!pq.empty()) {
		pii nx = pq.top();
		pq.pop();
		if (!same(now.second, nx.second)) {
			unite(now.second, nx.second);
			cnt--;
			ans += now.first + nx.first;
			if (cnt == 1) {
				cout << ans << endl;
				return 0;
			}
			if (!que.empty()) {
				now = que.front();
				que.pop();
			}
			else {
				now = pq.top();
				pq.pop();
			}

		}
		else {
			que.push(nx);
		}
		
	}
	cout << "Impossible" << endl;
	return 0;
}