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 heapq
from collections import deque


n, m = map(int, input().split())
a = list(map(int, input().split()))
info = [list(map(int, input().split())) for i in range(m)]
tree = [[] for i in range(n)]

for b, c in info:
    tree[b].append(c)
    tree[c].append(b)

visited = [False] * n
group = []
for i in range(n):
    if visited[i]:
        continue
    q = deque([i])
    visited[i] = True
    tmp = [a[i]]
    while q:
        pos = q.pop()
        for next_pos in tree[pos]:
            if visited[next_pos]:
                continue
            visited[next_pos] = True
            q.append(next_pos)
            tmp.append(a[next_pos])
    group.append(tmp)

for i in range(len(group)):
    group[i] = sorted(group[i])

ans = 0
cnt = len(group)*2 - 2

if cnt == 0:
    print(0)
    exit()
    
for i in range(len(group)):
    ans += group[i][0]
    cnt -= 1
    group[i][0] = 10**9 + 7

q = []
for i in range(len(group)):
    for num in group[i]:
        if num != 10**9 +7:
            heapq.heappush(q, num)

for i in range(cnt):
    if not q:
        print("Impossible")
        exit()
    ans += heapq.heappop(q)
print(ans)
    