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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;

public class D
{
	public static void Main() => (new Solver()).Solve();
}


public class Solver
{
	public void Solve()
	{
		int N = GetInt();
		int M = GetInt();
		long[] a = GetLongs(N);
		int[] x = new int[M];
		int[] y = new int[M];
		for(int i = 0; i < M; i++)
		{
			x[i] = GetInt();
			y[i] = GetInt();
		}

		var uf = new UnionFind(N);
		for(int i = 0; i < M; i++)
		{
			if(!uf.IsSame(x[i], y[i]))
				uf.Merge(x[i], y[i]);
		}

		var set = new HashSet<int>();
		for(int i = 0; i < N; i++)
			set.Add(uf.Root(i));

		var root = set.ToList();
		var dict = new Dictionary<int, List<long>>();
		for(int i = 0; i < root.Count; i++)
			dict[root[i]] = new List<long>();
		
		for(int i = 0; i < N; i++)
			dict[uf.Root(i)].Add(a[i]);

		for(int i = 0; i < root.Count; i++)
			dict[root[i]].Sort();

		var pq = new PriorityQueue<long>(N, (s, t) => s.CompareTo(t));
		foreach(var c in dict[root[0]])
			pq.Push(c);

		long ans = 0;
		for(int i = 1; i < root.Count; i++)
		{
			if(pq.Size == 0)
			{
				WriteLine("Impossible");
				return;
			}

			ans += pq.Pop() + dict[root[i]][0];
			for(int j = 1; j < dict[root[i]].Count; j++)
				pq.Push(dict[root[i]][j]);
		}

		WriteLine(ans);
	}
}

public class UnionFind
{
	private int[] par = null;
	private int[] rank = null;
	private int[] ccSize = null;
	
	public UnionFind(int n)
	{
		par = new int[n];
		rank = new int[n];
		ccSize = new int[n];
		for(int i = 0; i < n; i++)
		{
			par[i] = i;
			rank[i] = 0;
			ccSize[i] = 1;
		}
	}

	public bool IsSame(int x, int y)
	{
		return (Root(x) == Root(y));
	}

	public int Root(int x)
	{
		if(par[x] == x)
			return x;

		int r = Root(par[x]);
		par[x] = r;
		return r;
	}
	
	public bool Merge(int x, int y)
	{
		int rx = Root(x);
		int ry = Root(y);
		if(rx == ry)
			return false;
		
		if(rank[rx] < rank[ry])
		{
			int tmp = rx;
			rx = ry;
			ry = tmp;
		}
		else if(rank[rx] == rank[ry])
			rank[rx]++;

		par[ry] = rx;
		ccSize[rx] = ccSize[rx] + ccSize[ry];
		return true;
	}

	public int Size(int x)
	{
		return ccSize[Root(x)];
	}
}

public class PriorityQueue<T>
{
	public long Size { get; private set; } = 0;
	public long MaxSize { get; private set; } = 0;
	private T[] m_heap;
	private Comparison<T> Comp = null;
	
	public PriorityQueue(long maxSize, Comparison<T> comp)
	{
		if(maxSize <= 0)
			throw new Exception();
		MaxSize = maxSize;
		m_heap = new T[maxSize];

		Comp = comp;
	}
	
	public void Push(T x)
	{
		if(Size == MaxSize)
		{
			T[] new_heap = new T[MaxSize << 1];
			Array.Copy(m_heap, new_heap, MaxSize);
			m_heap = new_heap;
			MaxSize <<= 1;
		}
		
		long i = Size++;
		while(i > 0)
		{
			long p = (i - 1)/2;
			if(Comp(m_heap[p], x) <= 0)
				break;
			m_heap[i] = m_heap[p];
			i = p;			
		}
		m_heap[i] = x;		
	}
	
	public T Pop()
	{
		if(Size == 0)
			throw new Exception("Queue is empty.");
		
		T result = m_heap[0];
		T x = m_heap[--Size];
		long i = 0;
		while(i * 2 + 1 < Size)
		{
			long c1 = i * 2 + 1, c2 = i * 2 + 2;
			if(c2 < Size && Comp(m_heap[c2], m_heap[c1]) < 0)
				c1 = c2;
			if(Comp(m_heap[c1], x) >= 0)
				break;
			m_heap[i] = m_heap[c1];
			i = c1;
		}
		m_heap[i] = x;
		
		return result;		
	}	
}

public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(int N) => Enumerable.Range(0, N).Select(_ => GetInt()).ToArray();
	public static long[] GetLongs(int N) => Enumerable.Range(0, N).Select(_ => GetLong()).ToArray();
	public static double[] GetDoubles(int N) => Enumerable.Range(0, N).Select(_ => GetDouble()).ToArray();
	public static string[] GetStrings(int N) => Enumerable.Range(0, N).Select(_ => GetString()).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) < 0)
			x = y;
	}

	public static void chmin<T>(ref T x, T y) where T : IComparable<T>
	{
		if(x.CompareTo(y) > 0)
			x = y;
	}

	public static void swap<T>(ref T x, ref T y)
	{
		T tmp = x;
		x = y;
		y = tmp;
	}
}