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 <bits/stdc++.h>
using namespace std;

#define PI acos(-1.0)
#define INF 1e18
#define inf 0x3f3f3f3f
#define FAST_IO ios::sync_with_stdio(false)

const int N=123456;
typedef long long LL;
vector <int> E[N];
int w[N],vis[N];
int bestidx,bestval;

void dfs(int x){
    vis[x]=1;
    if(w[x]<bestval){
        bestval=w[x];
        bestidx=x;
    }
    for(auto u:E[x]){
        if(!vis[u]) dfs(u);
    }
}

int main(){
    LL ans=0;
    int n,m,cnt=0;
    scanf("%d %d",&n,&m);
    for(int i=0;i<n;i++) scanf("%d",&w[i]);
    for(int i=1;i<=m;i++){
        int x,y;
        scanf("%d %d",&x,&y);
        E[x].push_back(y);
        E[y].push_back(x);
    }
    for(int i=0;i<n;i++){
        if(!vis[i]){
            bestval=2e9;
            dfs(i);
            ans+=bestval;
            w[bestidx]=2e9;
            cnt++;
        }
    }
    if(cnt==1) {printf("0\n");return 0;}
    sort(w,w+n);
    for(int i=0;i<cnt-2;i++){
        if(w[i]==2e9){
            printf("Impossible\n");
            return 0;
        }
        ans+=w[i];
    }
    printf("%lld\n",ans);
    return 0;
}