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)

from heapq import heappush, heappop, heapify

N, M = map(int, input().split())
costs = [[x] for x in list(map(int, input().split()))]
for i in range(N):
  heapify(costs[i])

# union-find
parent = list(range(N))
rank = [0] * (N)

def getRoot(x):
  if parent[x] == x:
    return x
  else:
    # ルートに繋ぎ変える
    parent[x] = getRoot(parent[x])
    return parent[x]

def unite(x, y, pop=True):
  global costs
  xRoot = getRoot(x)
  yRoot = getRoot(y)
  if xRoot == yRoot:
    print('error!')
    exit()
  #print(costs, xRoot, yRoot)
  cost = costs[xRoot][0] + costs[yRoot][0]
  if pop:
    heappop(costs[xRoot])
    heappop(costs[yRoot])
  if rank[xRoot] < rank[yRoot]:
    parent[xRoot] = yRoot
    costs[yRoot] += costs[xRoot]
    heapify(costs[yRoot])
    return cost, yRoot
  else:
    parent[yRoot] = xRoot
    costs[xRoot] += costs[yRoot]
    heapify(costs[xRoot])
    if rank[xRoot] == rank[yRoot]:
      rank[xRoot] += 1
    return cost, xRoot

for i in range(M):
  x, y = map(int, input().split())
  unite(x, y, False)

forestheap = []
for i in range(N):
  if parent[i] == i:
    heappush(forestheap, (costs[i][0], i))

ans = 0
while len(forestheap) > 1:
  c1, v1 = heappop(forestheap)
  c2, v2 = heappop(forestheap)
  cost, newRoot = unite(v1, v2)
  ans += cost
  # 使えるノードがなくなって、まだ連結でなければ失敗
  if len(costs[newRoot]) == 0:
    print('Impossible')
    exit()
  heappush(forestheap, (costs[newRoot][0], newRoot))

print(ans)