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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <cstdio>
#include <cstring>
#include <algorithm>
#define ll long long
//#define mod 1000000007
#define MN 100005
using namespace std;
int a[MN],pos[MN],hua[MN];
int n,m,tot;
bool u[MN];
ll sum;

inline int read()
{
	int n=0,f=1; char c=getchar();
	while (c<'0' || c>'9') {if(c=='-')f=-1; c=getchar();}
	while (c>='0' && c<='9') {n=n*10+c-'0'; c=getchar();}
	return n*f;
}

//inline void rw(int& x,int y) {x+=y; if (x>=mod)x-=mod;}
int getf(int x) {return hua[x]<0?x:hua[x]=getf(hua[x]);}
inline void gather(int x,int y) {if (a[-hua[x]]<a[-hua[y]]) hua[y]=hua[x]; hua[x]=y;}
bool cmp(int x,int y) {return a[x]<a[y];}

int main()
{
	register int i,x,y;
	n=read(); m=read(); tot=(n-1-m)*2;
	if (tot>n) return 0*printf("Impossible");
	if (!tot) return 0*printf("0");
	for (i=1;i<=n;++i) a[i]=read(),pos[i]=i,hua[i]=-i;
	for (i=1;i<=m;++i)
	{
		x=read()+1; y=read()+1;
		gather(getf(x),getf(y));
	}
	for (i=1;i<=n;++i)
		if (hua[i]<0) u[-hua[i]]=true,sum+=a[-hua[i]],--tot;
	sort(pos+1,pos+n+1,cmp);
	for (i=1;i<=n&&tot;++i)
		if (!u[pos[i]]) sum+=a[pos[i]],--tot;
	printf("%lld",sum);
}