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++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using ll = long long;
using namespace std;
#define rep(i,n) for(int i=0, i##_len=(int)(n); i<i##_len; i++)
#define reps(i,n) for(int i=1 , i##_len=(int)(n);i<=i##_len;i++)
#define rrep(i,n) for(int i=((int)(n)-1);i>=0;i--)
#define rreps(i,n) for(int i=((int)(n));i>0;i--)
#define repi(i,x) for(auto i=(x).begin(),i##_fin=(x).end();i!=i##_fin;i++)
#define all(x) (x).begin(), (x).end()
#define input(array) repi(array##_itr, array) { cin >> *(array##_itr); }
#define F first
#define S second
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back
string solve(bool a) { return ((a) ? "Yes" : "No"); }
typedef vector<int> Vi;
typedef vector<Vi> VVi;
typedef pair<int , int> Pi;
typedef vector<Pi> VPi;
typedef vector<long long> V;
typedef vector<V> VV;
typedef pair<long long , long long> P;
typedef vector<P> VP;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1;} return 0;}
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1;} return 0;}
const long long INFLL = 1LL<<60;
const int INF = 1<<30;
const double PI=acos(-1);
//union by size + path having
class UnionFind{
	public:
	vector<long long> par; // 各元の親を表す配列
	vector<long long> siz; // 素集合のサイズを表す配列(1 で初期化)
	

	// Constructor
	UnionFind(long long sz_) : par(sz_), siz(sz_,1LL){
		for (long long i = 0; i < sz_; ++i)
		par[i] = i; // 初期では親は自分自身
	}
	void init(long long sz_){
		par.resize(sz_);
		siz.assign(sz_,1LL); // resize だとなぜか初期化されなかった
		for (long long i = 0; i < sz_; ++i)
			par[i] = i; // 初期では親は自分自身
	}
	// Member Function


	// Find
	long long root(long long x){ // 根の検索
		while (par[x] != x){
			x = par[x] = par[par[x]]; // x の親の親を x の親とする
		}
		return x;
	}
	// 結合(Unite, Merge)
	bool merge(long long x, long long y){
		x = root(x);
		y = root(y);
		if (x == y){
			return false;
		}
		// merge technique（データ構造をマージするテク．小を大にくっつける）
		if (siz[x] < siz[y]){
			swap(x, y);
		}
		siz[x] += siz[y];
		par[y] = x;
		return true;
	}


	// 連結判定(つながっているときはture,つながっていなければfalse)
	bool issame(long long x, long long y){ 
		return root(x) == root(y);
	}


	// 素集合のサイズ
	long long size(long long x){ 
		return siz[root(x)];
	}
};
int main(){
	int n,m;
	ll ans=0LL;
	cin >>n>>m;
	V a(n);
	input(a);
	VPi path(m);
	
	rep(i, m) { cin >> path[i].F >> path[i].S; }
	UnionFind dis(n);
	int bind = 0;
	priority_queue<pair<ll, int>> q,tmp;

	pair<ll, int> at;
	rep(i, m) {
		if (dis.merge(path[i].F, path[i].S)) {
			bind++;

		}
	}
	clog<<bind<<endl;
	if (n - 1 - bind > bind) {
		cout << "Impossible" << endl;
		return 0;
	}
	return -1;
	rep(i, n) { q.push(mp(a[i], i)); }
	//	cout<<ans<<endl;
}