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 <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <vector>
#include <queue>
#include <stack>
#include <algorithm>
#include <map>
#include <set>
#include <cmath>
#include <stdlib.h>
#include <functional>
#define ll long long
#define llu unsigned long long
#define INF 0x3f3f3f3f
#define LINF 0x3f3f3f3f3f3f3f3f
using namespace std;
const int N = 1e5 + 10;
int n, m;
ll cost[N];
bool vis[N];
vector<pair<ll, int>> vec;
vector<vector<pair<ll, int>>> L;
vector<int> vt;
int P[N];

int _find(int x) {
	return P[x] = (P[x] != x ? _find(P[x]) : x);
}

void merge(int x, int y) {
	P[_find(y)] = _find(x);
}

int newidx(int x) {
	return lower_bound(vt.begin(), vt.end(), x) - vt.begin();
}

int main()
{
	int i, j, k, x, y;
	scanf("%d%d", &n, &m);

	for (i = 0; i < n; ++i) {
		scanf("%lld", &cost[i]);
		P[i] = i;
		vec.push_back({ cost[i], i });
	}

	sort(vec.begin(), vec.end());
	
	for (i = 0; i < m; ++i) {
		scanf("%d%d", &x, &y);
		merge(x, y);
	}

	
	for (i = 0; i < n; ++i) {
		vt.push_back(_find(i));
	}

	sort(vt.begin(), vt.end());
	vt.erase(unique(vt.begin(), vt.end()), vt.end());

	L.resize(vt.size());
	for (i = 0; i < n; ++i) {
		L[newidx(_find(i))].push_back({ cost[i], i });
	}

	for (i = 0; i < L.size(); ++i) sort(L[i].begin(), L[i].end());

	ll sum = 0;
	int cnt = L.size();

	if (n < 2 * (L.size() - 1)) {
		printf("Impossible\n");
		return 0;
	}
	if (cnt == 1) {
		printf("0\n");
		return 0;
	}

	for (i = 0; i < L.size(); ++i) {
		vis[L[i][0].second] = true;
		sum += L[i][0].first;
		cnt++;
	}

	if (cnt == 2) {
		printf("%lld\n", sum);
		return 0;
	}

	int lim = 2*L.size() - 2;

	for (i = 0; i < vec.size(); ++i) {
		if (!vis[vec[i].second]) {
			sum += vec[i].first;
			cnt++;
			if (cnt >= lim) break;
		}
	}
	
	printf("%lld\n", sum);

}