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 Python (3.4.3) (judge verdict: Wrong Answer)


import heapq

n, m = map(int, input().split())
a = list(map(int, input().split()))

qs = {}
graph = [[] for x in range(n)]
for i in range(m):
    _from, _to = map(int, input().split())
    graph[_from].append(_to)
    graph[_to].append(_from)

visited = [False for x in range(n)]
# print(graph)

for i in range(n):
    first = i
    if visited[i]:
        continue
    que = [[first]]
    q_target = qs.get(first) or []
    while que:
        targets = que.pop()
        for next_target in targets:
            if not visited[next_target]:
                q_target.append(a[next_target])
                visited[next_target] = True
                que.append(graph[next_target])

    q_target.sort()
    qs[first] = q_target
    # print(i)
    # print(visited)
    # print(qs[first])

# print("====")
# print(qs)
# print("====")
cost = 0
first = 0
def impossible():
    print("Impossible")
    __import__("sys").exit()