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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
input = sys.stdin.readline
n,m = map(int,input().split())
cost = list(map(int,input().split()))
ab = [list(map(int, input().split(' '))) for i in range(m)]
graph = [[] for i in range(n)]
visited = [0 for i in range(n)]
vers = []
for a,b in ab:
  graph[a].append(b)
  graph[b].append(a)
for i in range(n):
  if visited[i] == 0:
    vers.append([])
    stack = [i]
    while stack:
      x = stack.pop()
      visited[x] = 1
      vers[-1].append((cost[x],x))
      for y in graph[x]:
        if visited[y] == 0:
          stack.append(y)
n_grph = len(vers)
if (n_grph-1)*2 > n:
  print("Impossible")
  exit()
for ver in vers:
  ver.sort()
visited = [0 for i in range(n)]
i = [i for i in range(n)]
costi = list(zip(cost,i))
costi.sort()
ans = 0
t = n_grph-2
if t >= 0:
  for ver in vers:
    ans += ver[0][0]
    visited[ver[0][1]] = 1

k = 0
while t > 0:
  c = costi[k][1]
  if visited[c] == 0:
    ans += costi[k][0]
    t -= 1
  k += 1
print(ans)