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: Wrong Answer)

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
int n,m,now,ans=0;
struct node{
	int a;
	bool vis;
}a[100010];
int fa[100010],mi[100010];
void init(){
	now=n;
	for(int i=0;i<=n;++i)  fa[i]=i,mi[i]=i;
}
int find(int x){
	if(fa[x]==x)  return fa[x];
	else  return fa[x]=find(fa[x]);
}
bool cmp(node b,node c){
	return b.a<c.a;
}
int main(){
	scanf("%d%d",&n,&m);
	int i,j;
	for(i=0;i<n;++i){
		scanf("%d",&a[i].a);
	}
	init();
	int x,y;
	for(i=1;i<=m;++i){
		scanf("%d%d",&x,&y);
		int fx=find(x),fy=find(y);
		if(fx!=fy){
			fa[fx]=fy;now--;
			if(a[mi[fx]].a<a[mi[fy]].a)  mi[fy]=mi[fx];
		}
	}
	if(now==1){
		printf("0\n");return 0;
	}
	if((now-1)*2>n){
		printf("Impossible\n");return 0;
	}
	for(i=0;i<n;++i){
		int xx=find(i);
		a[mi[xx]].vis=true;
	}
	sort(a,a+n,cmp);
	int al=(now-1)*2-now,st=0;
	while(al>0){
		if(a[st].vis){
			st++;continue ;
		}
		ans+=a[st].a;
		st++;al--;
	}
	for(i=0;i<n;++i){
		if(a[st].vis)  ans+=a[st].a;
	}
	printf("%d\n",ans);
	return 0;
}