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
import sys
sys.setrecursionlimit(10**7)
from collections import deque

n,m = map(int,input().split())
if m == n-1:
  print(0)
  exit()
if 2*(n-m-1) > n:
    print("Impossible")
    exit()

e = [[] for i in range(n)]
a = list(map(int,input().split()))
for i in range(m):
    x,y = map(int,input().split())
    e[x].append(y)
    e[y].append(x)

def dfs(x):
    l = []
    d[x] = 1
    l.append(a[x])
    q = deque([])
    q.append(x)
    while q:
        now = q.pop()
        for nex in e[now]:
            if d[nex] > 0:
                continue
            l.append(a[nex])
            d[nex] = 1
            q.append(nex)
    l.sort()
    ans = l[0]
    
    for i in l[1:]:
        h.append(i)
    return ans
count = 2*(n-m-1)
d = [-1]*n
ans = 0
h = []
for i in range(n):
    if d[i] < 0:
        ans += dfs(i)
        count -= 1
if count > 0:
    h.sort()
    ans += sum(h[:count])
print(ans)

