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 (2.7.6) (judge verdict: Wrong Answer)

n, m = map(int, raw_input().split())

a = map(int, raw_input().split())

x=[]
y=[]
for i in range(m):
   x0, y0 =map(int, raw_input().split())
   x.append(x0)
   y.append(y0)

g=[-1]*n

for i in range(m):
   if (g[x[i]]==-1 and g[y[i]]==-1 ):
      g[x[i]]=x[i]
      g[y[i]]=x[i]
   if (g[x[i]]==-1 and g[y[i]]<>-1 ):
      g[x[i]]=g[y[i]]
   if (g[x[i]]<>-1 and g[y[i]]==-1 ):
      g[y[i]]=g[x[i]]
   if (g[x[i]]<>-1 and g[y[i]]<>-1 ):
      b=g[x[i]]
      c=g[y[i]]
      for j in range(m):
         if g[j]==b : g[j]=c
     
f=set(g)
if (len(f)==2):
   e=[]
   for d in f:
      e.append(d)
   r=[]
   s=[]
   for j in range(n):
      if g[j]==e[1] : s.append(j)
      if g[j]==e[0] : r.append(j)

   minc=a[r[0]]+a[s[0]]
   for j in r:
      for k in s:
         if minc>a[j]+a[k] :minc=a[j]+a[k]
   print minc
         
else:
   print "Impossible"