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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"container/heap"
	"fmt"
	"os"
	"strconv"
)

func getScanner(fp *os.File) *bufio.Scanner {
	scanner := bufio.NewScanner(fp)
	scanner.Split(bufio.ScanWords)
	scanner.Buffer(make([]byte, 1000005), 1000005)
	return scanner
}

func getNextString(scanner *bufio.Scanner) string {
	scanner.Scan()
	return scanner.Text()
}

func getNextInt(scanner *bufio.Scanner) int {
	i, _ := strconv.Atoi(getNextString(scanner))
	return i
}

func getNextInt64(scanner *bufio.Scanner) int64 {
	i, _ := strconv.ParseInt(getNextString(scanner), 10, 64)
	return i
}

func getNextUint64(scanner *bufio.Scanner) uint64 {
	i, _ := strconv.ParseUint(getNextString(scanner), 10, 64)
	return i
}

func getNextFloat64(scanner *bufio.Scanner) float64 {
	i, _ := strconv.ParseFloat(getNextString(scanner), 64)
	return i
}

func main() {
	fp := os.Stdin
	wfp := os.Stdout
	cnt := 0

	if os.Getenv("MASPY") == "ますピ" {
		fp, _ = os.Open(os.Getenv("BEET_THE_HARMONY_OF_PERFECT"))
		cnt = 2
	}
	if os.Getenv("MASPYPY") == "ますピッピ" {
		wfp, _ = os.Create(os.Getenv("NGTKANA_IS_GENIUS10"))
	}

	scanner := getScanner(fp)
	writer := bufio.NewWriter(wfp)
	solve(scanner, writer)
	for i := 0; i < cnt; i++ {
		fmt.Fprintln(writer, "-----------------------------------")
		solve(scanner, writer)
	}
	writer.Flush()
}

func solve(scanner *bufio.Scanner, writer *bufio.Writer) {
	n := getNextInt(scanner)
	m := getNextInt(scanner)
	aa := make([]int, n)
	ee := n - 1 - m
	if ee == 0 {
		fmt.Fprintln(writer, 0)
		return
	}
	ee <<= 1
	for i := 0; i < n; i++ {
		aa[i] = getNextInt(scanner)
	}
	uf := make([]int, n)
	for i := 0; i < n; i++ {
		uf[i] = i
	}
	for i := 0; i < m; i++ {
		x := getNextInt(scanner)
		y := getNextInt(scanner)
		rx := root(x, uf)
		ry := root(y, uf)
		if rx == ry {
			continue
		}
		uf[ry] = rx
	}
	nn := make([]nodes, n)
	for i := 0; i < n; i++ {
		heap.Init(&nn[i])
	}
	for i := 0; i < n; i++ {
		r := root(i, uf)
		heap.Push(&nn[r], node{
			i: r,
			a: aa[i],
		})
	}
	h := &nodes{}
	var ans int64
	for i := 0; i < n; i++ {
		if nn[i].Len() == 0 {
			continue
		}
		p := heap.Pop(&nn[i]).(node)
		ans += int64(p.a)
		ee--
		for nn[i].Len() > 0 {
			heap.Push(h, heap.Pop(&nn[i]).(node))
		}
	}
	for ee > 0 && h.Len() > 0 {
		p := heap.Pop(h).(node)
		ans += int64(p.a)
		ee--
	}

	if ee > 0 {
		fmt.Fprintln(writer, "Impossible")
		return
	}

	fmt.Fprintln(writer, ans)
}

type node struct {
	i, a int
}
type nodes []node

func (h nodes) Len() int           { return len(h) }
func (h nodes) Less(i, j int) bool { return h[i].a < h[j].a }
func (h nodes) Swap(i, j int)      { h[i], h[j] = h[j], h[i] }
func (h *nodes) Push(x interface{}) {
	*h = append(*h, x.(node))
}
func (h *nodes) Pop() interface{} {
	old := *h
	n := len(old)
	x := old[n-1]
	*h = old[0 : n-1]
	return x
}

func root(i int, uf []int) int {
	if i == uf[i] {
		return i
	}
	uf[i] = root(uf[i], uf)

	return uf[i]
}