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 PyPy3 (2.4.0) (judge verdict: Runtime Error)

n,m=map(int,input().split())
a=list(map(int,input().split()))
r=[i for i in range(n)]
s=[0]*n
def f(x):
    if x==r[x]:
        return x
    x=r[x]
    return f(r[x])
def g(x,y):
    x=f(x)
    y=f(y)
    if s[x]>s[y]:
        r[y]=x
        s[x]+=s[y]
    else:
        r[x]=y
        s[y]+=s[x]
for i in range(m):
    x,y=map(int,input().split())
    g(x,y)
if n<2*(n-m-1):
    print("Impossible")
else:
    c={}
    for i in range(n):
        t=f(i)
        if t in c:
            c[t].append(a[i])
        else:
            c[t]=[a[i]]
    an=0
    q=[]
    for i in c.keys():
        an+=min(c[i])
        q+=sorted(c[i])[1:]
    if m!=n-1:
    	print(an+sum(sorted(q)[:2*(n-m-1)-n+m]))
    else:
        print(0)