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 <iostream>
#include <cstdio>
#include <string>
#include <algorithm>
#include <utility>
#include <cmath>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <numeric>
#include <functional>
using namespace std;
typedef long long ll;
typedef vector<ll> vl;
typedef vector<vector<ll>> vvl;
typedef pair<ll, ll> P;
#define rep(i, n) for(ll i = 0; i < n; i++)
#define exrep(i, a, b) for(ll i = a; i <= b; i++)
#define out(x) cout << x << endl
#define exout(x) printf("%.10f\n", x)
#define chmax(x, y) x = max(x, y)
#define chmin(x, y) x = min(x, y)
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define pb push_back
#define re0 return 0
const ll mod = 1000000007;
const ll INF = 1e16;
const ll MAX_N = 100010;

class UnionFind {
public:
    vl parent;  // 親ノード
    vl Siz;  // 集合の大きさ
    
    // コンストラクタ
    UnionFind(ll n): parent(n), Siz(n, 1) {
        rep(i, n) {
            parent[i] = i;
        }
    }

    // n要素で初期化
    void init(ll n) {
        parent.resize(n);
        Siz.assign(n, 1);
        rep(i, n) {
            parent[i] = i;
        }
    }

    // xの属する集合の根を求める
    ll root(ll x) {
        if(parent[x] == x) {
            return x;
        }
        else {
            return parent[x] = root(parent[x]);
        }
    }

    // xとyの属する集合を併合
    void unite(ll x, ll y) {
        x = root(x);
        y = root(y);
        if(x == y) {
            return;
        }
        if(Siz[x] < Siz[y]) {
            swap(x, y);
        }
        Siz[x] += Siz[y];
        parent[y] = x;
    }
    
    // xとyが同じ集合に属するかどうか
    bool same(ll x, ll y) {
        return root(x) == root(y);
    }

    // xの属する集合の要素数を求める
    ll size(ll x) {
        return Siz[root(x)];
    }
};
 
int main() {
    ll n, m;
    cin >> n >> m;

    vl a(n);
    rep(i, n) {
        cin >> a[i];
    }

    UnionFind Uni(n);
    Uni.init(n);
    rep(i, m) {
        ll x, y;
        cin >> x >> y;
        Uni.unite(x, y);
    }

    vvl G(n);
    ll u = 0;  // 連結成分の個数
    rep(v, n) {
        if(v == Uni.root(v)) {
            u++;
        }
        G[Uni.root(v)].pb(a[v]);
    }

    if(u == 1) {
        out(0);
        re0;
    }

    if(n < 2*(u-1)) {
        out("Impossible");
        re0;
    }

    ll ans = 0;
    vl w;
    rep(v, n) {
        if(v == Uni.root(v)) {
            sort(all(G[v]));
            ans += G[v][0];
            rep(i, G[v].size()) {
                if(i > 0) {
                    w.pb(G[v][i]);
                }
            }
        }
    }
    
    sort(all(w));
    rep(i, u-2) {
        ans += w[i];
    }
    
    out(ans);
    re0;
}