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 Ruby (2.3.3) (judge verdict: Wrong Answer)

nodes, edges = gets.chomp.split(' ').map(&:to_i)
costs = gets.chomp.split(' ').map(&:to_i)
edge_collection = []
edges.times do
  combine_index = -1
  edge = gets.chomp.split(' ').map(&:to_i)
  edge_collection.each.with_index do |an_edge, i|
    an_edge.each do |a_node|
      if edge.include?(a_node)
        if combine_index < 0
          an_edge.concat(edge)
          an_edge.uniq!
          combine_index = i
          break
        else
          an_edge.concat(edge_collection[combine_index])
          an_edge.uniq!
          edge_collection[combine_index] = []
          combine_index = i
          break
        end
      end
    end
  end
  edge_collection.push(edge) if combine_index < 0
end
edge_collection.delete([])
edge_collection.each do |an_edge|
  an_edge.sort_by!{|node|costs[node]}
end
edge_collection.sort_by!{|edge|costs[edge[0]]}
groups = edge_collection.length
if groups <= 0
  puts "Impossible"
  exit
end
count = 0
(groups - 1).times do
  break if edge_collection[0].length == 0
  count += costs[edge_collection[0].shift]
  count += costs[edge_collection[1].shift]
  edge_collection[0].concat(edge_collection[1])
  edge_collection[0].sort_by!{|node|costs[node]}
  edge_collection.delete_at(1)
end
if edge_collection.length > 1
  puts "Impossible"
else
  puts count
end