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)

/*
                                                                                                     
                                             `-:://:::-                                             
                                           `//:-------:/:`                                          
                                          .+:--.......--:+`                                         
                                         `+:--..`````..--//`                                        
                                         .o:--..`` ``..--:o`                                        
                                         .o:--...```..---+/`                                        
                                       `/y+o/---....---:+o.                                         
                                   `...````-os+/:---:/+o/--.`                                       
              `-/+++++/:.      `...`       :h+d+oooo+/+-`   ...                                     
            `/++//:::://++-`....`         -.`//````````:`     `..`                                  
           `o+/::------://o/`           `-` -.          -`       `..`                               
 `---.-o/:./o/::-..``..-ЗАПУСКАЕМ      ..  ..            -`        `...       ``..``                
  `....o+:-++/:--.```..-://s.        `-`  .-              -`          `-o: .-//::::/:-`             
          `:s+/:--....-::/+s-`      .-   `-                -`           -///:--------:/:`           
           ./s+//:::::://oo-``..НЕЙРОННУЮ: СЕТЬ:::::::-`РАБОТЯГИ        `+:--........--:/`          
            .:ooo+++++osso-`    `.:-...`/` ./::-------:/:`   -`         :+--..``````.--:+:...-+:-`  
             `.-/+++++/+-.-`    -.   ``:so:/:--.......--:+`  `-```````o+/+--..`````..--:o/-..:s+:.  
                 ```````:``.. `-`     -` `+:--..`````..--/+-.../.`````..-o:--.......---/o.    `     
                        `:  `:-      -.  .o:--..`` ``..--:o`   `-`      `:o+:--------:+o-`          
                         `-`-...    ..   .o/--...```..--:+/`    `-`     `oy/so/////++o/.`           
                          -/`  `-` `- ``+s/o/:---...---:++.      `-`   .-../d://///:-.`             
                `.---..``-..-    .-/..`````-oo+/:::::/+o+-        `-``-`  `-.  ````                 
             `:++++/+++++-  ..``.-/:`      /y-:/++o++/:.`..`       ./.   `-                         
            -++/::::::://+/..:-``:` ..   `-.`  ```.```    `..`   `..`-` `-                          
       ``  -o//:--....-::/++` -.-`   `-`.-`                 `..`..`  `-.-                           
  -----ss+:++/:--.```..-://s.  /.     `::                    `-:.     ./`                           
  `````/:..+o/::-..``.--:/+s. ..-`   `-``-`                 ..` `-`  `-`-`                          
          `-s+/::-----::/+oo---``-` ..    .:-    ```      .-`     .-.-  `-`                         
           `:oo+//::://+os/..:`..-/:`      :y.-:::::::.`.-`        ./-`  `-`                        
            `./+oooooooo+/.`-    .-:...`.. .//:-------://`        `- `..` `:.                       
              ``.-::::-.``-/`  `-` `-  `oo:+:--.......--:/`      `-    `.:--h.``..```               
                          -.-`.-    .-   `+:--..`````..--//`    `-       /s-//::::::::.             
                         -` `/-      ..  .o:--..`` ``..--:o.```.-        `//:--------://`           
                        -` .-`.-`     -.`-o/--...```..--:+/.``-:....``:-.+:--....`...--:+`          
                       ..`-.   `-.   ``:os:o/:---...---:++.  `-     ``///+:-..``````.--:+-````-.`   
              `.:///////.-`      .:-..` -``-+o+/:::::/+o/.  `-         `:+:-..`````..--:o/:--/ys+-  
            `-++///////+o/. ``....`-.    :` `.:++++++/:.`  .-           -o/---......---/o.   `.`    
           `++//:-----::/+o:..`     .-`   :    ```````    .-           `+so+:--------:++-`          
  `````:-``:o/::-..`..--:/+o`         -.  `-             .-          `../../+o+////+o+:.`           
  -----syo/o+/:--.```..-://s.          .-` `-           .-        `...     ``-:////:-``             
       .` `/s//:--....-::/+s.            -. `-`        .-       `..`                                
           .+o+/:::--:://+s/-..`          .::+y  ```  .-     `..`                                   
            ./oo++////+oso-`   `....       :y-+:::::::/`   ...                                      
             `.:+oooooo/-`         `....-. .//:-------:/:-.`                                        
                ``...``                 /+:+:--.......--:+`                                         
                                         `+:--..`````..--//`                                        
                                         .o:--..`` ``..--:o`                                        
                                         .+/--...```..--:+/`                                        
                                         `-o/:---...---:++.                                         
                                          `-+o+/:---:/+o/.                                          
                                            `.:+oooo+/-.`                                           
                                               ``````                                               
*/

#ifdef cheats
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#endif

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <map>
#include <set>
#include <queue>
#include <ostream>
#include <istream>
#include <typeinfo>
#include <iomanip>
#include <cstdio>
#include <cstdlib>
#include <cassert>
#include <limits>
#include <fstream>
#include <array>
#include <list>
#include <bitset>
#include <functional>
#include <random>
#include <cstring>

#define mt make_tuple
#define x first
#define y second
#define pb push_back
#define ppb pop_back
#define mp make_pair
#define umap unordered_map
#define uset unordered_set
#define elif else if
#define len(v) ((int)v.size())
#define f(i, n) for (int i = 0; i < (n); i++)
#define apply(v, act) for (auto &x : v) { act; }


using namespace std;

char string_in_buffer[(int)260];


void fast_scan(int &x) { scanf("%d", &x); }
void fast_scan(long long &x) { scanf("%lld", &x); }
void fast_scan(unsigned long long &x) { scanf("%llu", &x); }
void fast_scan(double &x) { scanf("%lf", &x); }
void fast_scan(long double &x) { scanf("%Lf", &x); }
void fast_scan(char &x) { 
	scanf("%c", &x); 
	if (x == '\n') {
		fast_scan(x);
	}
}
void fast_scan(string &x) {
	scanf("%s", string_in_buffer);
	x = string(string_in_buffer);
}

template<class TFirst, class TSecond>
void fast_scan(pair<TFirst, TSecond> &p) {
	fast_scan(p.first);
	fast_scan(p.second);
}

template <class T>
void fast_scan(vector<T> &v) {
	for (auto &x : v) fast_scan(x);
}

void fast_print(const int &x) { printf("%d", x); }
void fast_print(const long long &x) { printf("%lld", x); }
void fast_print(const unsigned long long &x) { printf("%llu", x); }
void fast_print(const double &x) { printf("%.15lf", x); }
void fast_print(const long double &x) { printf("%.15Lf", x); }
void fast_print(const char &x) { printf("%c", x); };
void fast_print(const string &x) { printf("%s", x.c_str());}

template<class TFirst, class TSecond>
void fast_print(const pair<TFirst, TSecond> &p) {
	fast_print(p.first);
	fast_print(' ');
	fast_print(p.second);
}

template <class T>
void fast_print(const vector<T> &v) {
	if (v.empty()) return;
	fast_print(v[0]);
	for (int i = 1; i < v.size(); i++) {
		fast_print(" ");
		fast_print(v[i]);
	}
}

template <class T>
void fast_print(const vector<vector<T>> &v) {
	if (v.empty()) return;
	fast_print(v[0]);
	for (int i = 1; i < v.size(); i++) {
		fast_print("\n");
		fast_print(v[i]);
	}
}



using namespace std;


namespace smart_io {
	string print_start = "";
	string sep = " ";
	bool first_print = false;

	void precall_print() {
		fast_print(print_start);
		print_start = "\n";
		first_print = true;
	}
} //namespace smart_io


template <class T>
ostream &operator,(ostream &os, const T &object) {
	if (!smart_io::first_print) {
		fast_print(smart_io::sep);
	} else {
		smart_io::first_print = false;
	}
	fast_print(object);
	return os;
}

template <class T>
istream &operator,(istream &is, T &object) {
	fast_scan(object);
	return is;
}

namespace typedefs {
	typedef long long ll;
	typedef unsigned long long ull;
	typedef pair<int, int> pii;
	typedef long double ld;
}

namespace numbers_operation {
	template<class T>
	T floor_mod(T a, T b) {
		if (a % b == 0) return 0;
		if (a >= 0 && b >= 0) return a % b;
		if (a <= 0 && b <= 0) return a % b;
		return abs(b) - (abs(a) % abs(b));
	}
}

using namespace numbers_operation;
using namespace typedefs;

#define print    \
smart_io::precall_print(); \
cout,

#define scan cin,

vector<vector<int>> g;

struct SUS {
	vector<int> up;
	vector<set<pii>> pep;
	set<pii> best;
	set<pii> ebal;
	vector<bool> can;

	SUS(int n, vector<int> cost) {
		up.resize(n);
		pep.resize(n);
		can.resize(n, true);

		f(i, n) {
			up[i] = i;
			pep[i].emplace(cost[i], i);
			best.emplace(cost[i], i);
			ebal.emplace(1, i);
		}
	}

	int get_root(int v) {
		if (up[v] == v) return v;
		return up[v] = get_root(up[v]);
	}

	void merge(int a, int b, bool del) {
		int _a = a;
		int _b = b;
		a = get_root(a);
		b = get_root(b);
		if (a == b) return;
		if (del) {
			can[_a] = can[_b] = false;
		}
		if (len(pep[a]) < len(pep[b])) {
			swap(a, b);	
		}
		up[b] = a;
		ebal.erase(mp(len(pep[a]), a));
		best.erase(*pep[a].begin());
		for (pii p : pep[b]) {
			pep[a].insert(p);
		}	
		best.erase(*pep[b].begin());
		while (!pep[a].empty()) {
			if (!can[pep[a].begin()->second]) {
				pep[a].erase(pep[a].begin());
			} else {
				break;
			}
		}
		if (!pep[a].empty()) {
			best.emplace(*pep[a].begin());
		}
		ebal.emplace(len(pep[a]), a);
	}
};

signed main(signed argc, char *argv[]) {
	int n, m;
	scan n, m;
	vector<int> cost(n);
	scan cost;
	SUS sus(n, cost);

	f(i, m) {
		int a, b;
		scan a, b;
		sus.merge(a, b, false);	
	}
	ll rez = 0;
	while (m++ < n - 1) {
		if (len(sus.best) < 2) {
			print "Impossible";
			return 0;
		}
		auto eb = sus.ebal.rbegin();
		auto it = sus.best.begin();
		pii s = *it;
		if (sus.get_root(it->second) == eb->second) {
			it++;
			s = *it;
		}
		pii f = *sus.pep[eb->second].begin();
		rez += f.first + s.first;
		sus.merge(f.second, s.second, true);
	}
	print rez;
}