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.

Examples

Input

7 5
1 2 3 4 5 6 7
3 0
4 0
1 2
1 3
5 6


Output

7


Input

5 0
3 1 4 1 5


Output

Impossible


Input

1 0
5


Output

0
from collections import*
from heapq import*
n,m,*a=map(int,open(0).read().split())
t=[-1]*n
def r(x):
  while t[x]>=0:x=t[x]
  return x
def u(x,y):
  x,y=r(x),r(y)
  if x!=y:
    if t[x]>t[y]:x,y=y,x
    t[x]+=t[y]
    t[y]=x
d=defaultdict(list)
for x,y in zip(*[iter(a[n:])]*2):u(x,y)
for i,v in enumerate(a[:n]):d[r(i)]+=v,
if len(d)<2:
  print(0)
  exit()
*d,=map(sorted,d.values())
c=sum(heappop(t)for t in d)
l=[]
for t in d:l+=t
i=len(d)-2
print(i>len(l)and'Impossible'or c+sum(sorted(l)[:i]))