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 collections, heapq
N, M = [int(_) for _ in input().split()]
A = [int(_) for _ in input().split()]
XY = [[int(_) for _ in input().split()] for _ in range(M)]
G = collections.defaultdict(list)
for x, y in XY:
    G[x] += [y]
    G[y] += [x]
B = sorted([v, i] for i, v in enumerate(A))
visited = [0] * N
ans = 0
H = []
t = 0
for b in B:
    v, i = b
    if not visited[i]:
        visited[i] = 1
        ans += v
        q = G[i]
        t += 1
        while q:
            i = q.pop()
            if not visited[i]:
                visited[i] = 1
                heapq.heappush(H, [A[i], i])
                q += G[i]
if len(H) < t - 2:
    print('Impossible')
    exit()
elif t == 1:
    print(0)
    exit()
for _ in range(t - 2):
    v, i = heapq.heappop(H)
    ans += v
print(ans)
