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<cmath>
#include<cstring>
#include<algorithm>
#include<queue>
#define ll long long
using namespace std;

const int N=100005;

struct node{
	int id,w;
	node(){}
	node(int id,int w):id(id),w(w){}
	friend bool operator<(node a,node b){
		return a.w>b.w;
	}
};
int n,m,x,y,r1,r2,cnt,sum;
ll ans;
int a[N],f[N],sz[N];
priority_queue<node> q1;
priority_queue<int,vector<int>,greater<int> > q2[N];

int find(int k){
	if (f[k]!=k) f[k]=find(f[k]);
	return f[k];
}

int main(){
	int i; node k1,k2;
	scanf("%d%d",&n,&m);
	for (i=1;i<=n;i++) scanf("%d",&a[i]);
	for (i=1;i<=n;i++) f[i]=i,sz[i]=1;
	for (i=1;i<=m;i++){
		scanf("%d%d",&x,&y); x++; y++;
		r1=find(x); r2=find(y);
		if (r1!=r2){
			if (sz[r1]>sz[r2]) swap(r1,r2);
			sz[r2]+=sz[r1];
			f[r1]=r2;
		}
	}
	for (i=1;i<=n;i++) q2[find(i)].push(a[i]);
	for (i=1;i<=n;i++)
		if (find(i)==i){
			if (sz[i]>1) q1.push(node(i,q2[i].top()));
			else sum++,ans+=1ll*a[i];
			cnt++;
		}
	if (cnt==1){
		printf("0\n");
		return 0;
	}
	if ((cnt-1)*2>n){
		printf("Impossible\n");
		return 0;
	}
	while (!q1.empty()){
		k1=q1.top(); q1.pop();
		if (q1.empty()){
			x=k1.id;
			for (i=1;i<=sum;i++){
				ans+=1ll*q2[x].top();
				q2[x].pop();
			}
			break;
		}
		k2=q1.top(); q1.pop();
		ans+=1ll*(k1.w+k2.w);
		x=k1.id; y=k2.id;
		q2[x].pop(); q2[y].pop();
		r1=find(x); r2=find(y);
		if (sz[r1]>sz[r2]) swap(r1,r2);
		sz[r2]+=sz[r1];
		f[r1]=r2;
		while (!q2[r1].empty()){
			q2[r2].push(q2[r1].top());
			q2[r1].pop();
		}
		q1.push(node(r2,q2[r2].top()));
	}
	printf("%lld\n",ans);
	return 0;
}