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: Runtime Error)

import numpy as np
from collections import deque
import heapq
n, m = map(int, input().split())
costs = list(enumerate(list(map(int, input().split()))))
que = deque(range(n))
vortexs = [[] for i in range(n)]
if n == 1:
    print("0")
    exit()
for i in range(m):
    l, r = map(int, input().split())
    vortexs[r].append(l)
    vortexs[l].append(r)
trees = []
def dfs(now, li, queue = deque()):
    if not li:
        li = []
    if now in que:
        que.remove(now)
        li.append(costs[now])
        for j in vortexs[now]:
            if j in que:
                queue.append(j)
        while queue:
            dfs(queue.popleft(), li, queue)
        return sorted(li, key=lambda x: x[1])
for i in range(n):
    if i in que:
        trees.append(dfs(i, []))
ans = 0
if len(trees) == 1:
    print("0")
for i in range(len(trees) - 1):
    ans += trees[i][0][1]
    ans += trees[i + 1][0][1]
    trees[i].pop(0)
    trees[i + 1].pop(0)
    if len(trees[i]) == 1:
        print("Impossible")
        exit()
print(ans)