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
input = sys.stdin.buffer.readline
from collections import defaultdict
import heapq

def main():
    N,M = map(int,input().split())
    a = list(map(int,input().split()))
    d = defaultdict(list)
        
    I = [i for i in range(N)]
    rank = [1 for _ in range(N)]
    def root(a):
        if I[a] == a:
            return a
        else:
            I[a] = root(I[a])
            return I[a]
            
    def unite(a,b):
        pa,pb = root(a),root(b)
        ra,rb = rank[a],rank[b]
        if ra > rb:
            I[pb] = pa
        else:
            I[pa] = pb
            if ra == rb:
                rank[pb] += 1
    
    for _ in range(M):
        x,y = map(int,input().split())
        unite(x,y)
        parent = root(x)
    
    for i,num in enumerate(I):
        parent = root(num)
        heapq.heappush(d[parent],a[i])
        
    if M == N-1:
        print(0)
        exit()
    elif N < 2*(N-M-1):
        print("Impossible")
        exit()

    l = len(d.keys())
    ans = 0
    rest = []
    for use in d.values():
        ans += heapq.heappop(use)
        rest.extend(use)

    remain = 2*(N-M-1)-l
    rest.sort()
    ans += sum(rest[:remain])
    
    print(ans)
    
if __name__ == "__main__":
    main()
