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: Accepted)

#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<vector>
#include<queue>
#include<bitset>
#include<string>
#include<stack>
#include<set>
#include<unordered_set>
#include<map>
#include<unordered_map>
#include<cstring>
#include<complex>
#include<cmath>
#include<iomanip>
#include<numeric>
#include<algorithm>
#include<list>
#include<functional>
#include<cassert>
#define mp make_pair
#define pb push_back
#define X first
#define Y second
#define y0 y12
#define y1 y22
#define INF 1987654321
#define PI 3.141592653589793238462643383279502884
#define fup(i,a,b,c) for(int (i)=(a);(i)<=(b);(i)+=(c))
#define fdn(i,a,b,c) for(int (i)=(a);(i)>=(b);(i)-=(c))
#define MEM0(a) memset((a),0,sizeof(a));
#define MEM_1(a) memset((a),-1,sizeof(a));
#define ALL(a) a.begin(),a.end()
#define SYNC ios_base::sync_with_stdio(false);cin.tie(0)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int, int> Pi;
typedef pair<ll, ll> Pll;
typedef pair<double, double> Pd;
typedef vector<int> Vi;
typedef vector<ll> Vll;
typedef vector<double> Vd;
typedef vector<Pi> VPi;
typedef vector<Pll> VPll;
typedef vector<Pd> VPd;
typedef tuple<int, int, int> iii;
typedef tuple<ll, ll, ll> LLL;
typedef vector<iii> Viii;
typedef vector<LLL> VLLL;
typedef complex<double> base;
const ll MOD = 998244353;
ll POW(ll a, ll b, ll MMM = MOD) {ll ret=1; for(;b;b>>=1,a=(a*a)%MMM)if(b&1)ret=(ret*a)% MMM; return ret; }
ll gcd(ll a, ll b) { return b ? gcd(b, a%b) : a; }
ll lcm(ll a, ll b) { if (a == 0 || b == 0)return a + b; return a*(b / gcd(a, b)); }
int dx[] = { 0,1,0,-1,1,1,-1,-1 }, dy[] = { 1,0,-1,0,1,-1,1,-1 };

char s[5]="RGBY";
ll a[100000];
int parent[100000];
int find(int a)
{
	if (parent[a] < 0)return a;
	return parent[a] = find(parent[a]);
}
void merge(int a, int b)
{
	a = find(a), b = find(b);
	if (a != b)
	{
		parent[a] += parent[b];
		parent[b] = a;
	}
}
map<int,Vll> M;
int main() {
	int n,m;
	scanf("%d%d",&n,&m);
	if(m==n-1)return !printf("0");
	if(n<2*(n-m-1))return !printf("Impossible");
	MEM_1(parent);
	fup(i,0,n-1,1)scanf("%lld",a+i);
	fup(i,0,m-1,1)
	{
		int x,y;
		scanf("%d%d",&x,&y);
		merge(x,y);
	}
	fup(i,0,n-1,1)
		M[find(i)].pb(a[i]);
	ll ans=0;
	int cnt=0;
	priority_queue<ll,Vll,greater<ll> > q;
	for(auto it=M.begin();it!=M.end();it++)
	{
		Vll &v=it->Y;
		sort(ALL(v));
		ans+=v[0],cnt++;
		fup(i,1,(int)v.size()-1,1)q.push(v[i]);
	}
	while(cnt<2*(n-m-1))
	{
		ans+=q.top();
		q.pop();
		cnt++;
	}
	printf("%lld",ans);
}