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 <bits/stdc++.h>
//#include "rail.h"
#define F first
#define S second
#define P push
#define pb push_back
#define MEM(dp,i) memset(dp,i,sizeof(dp))
#define W while
#define R return
#define C continue
#define SI size()
#define ll long long
#define ld long double
#define pll pair<ll,ll>
#define pii pair<int,int>
#define SF(x) scanf("%Id",&x)
#define SF2(x,y) scanf("%Id%Id",&x,&y)
#define SF3(x,y,z) scanf("%I64d%I64d%I64d",&x,&y,&z)
#define SF4(x,y,z,o) scanf("%I64d%I64d%I64d%I64d",&x,&y,&z,&o)
#define all(v) v.begin(),v.end()

using namespace std;
const long long INF = 1e16;
const long long MOD = 1e9+7;
const int MAX=100015;
vector<int> adj[MAX];
vector<pii> v;
int G[MAX];
bool vis[MAX];
int cur[MAX];
int g=0;
void DFS(int ver){
    if(vis[ver])R;
    vis[ver]=1;
    G[ver]=g;
    for(auto i : adj[ver]){
        DFS(i);
    }
}
int main(){
    int n,m;
    cin>>n>>m;
    if(m*2<n-2){cout<<"Impossible"; R 0;}
    int x;
    for(int i=0;i<n;i++){
        cin>>x;
        v.pb({x,i});
    }
    sort(v.begin(),v.end());
    for(int i=0;i<m;i++){
        int a,b;
        cin>>a>>b;
        adj[a].pb(b);
        adj[b].pb(a);
    }
    for(int i=0;i<n;i++){
        if(vis[i])continue;
        DFS(i);
        g++;
    }
    ll d=g+g-2,res=0,z;
    for(auto i : v){
        if(d==0)break;
        x=G[i.S];
        if(cur[x]>=g-1)continue;
        cur[x]++;
        z=i.F;
        res+=z;
        d--;
    }
    cout<<res;
}