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.

Examples

Input

7 5
1 2 3 4 5 6 7
3 0
4 0
1 2
1 3
5 6


Output

7


Input

5 0
3 1 4 1 5


Output

Impossible


Input

1 0
5


Output

0
#include <bits/stdc++.h>
using namespace std;

using ll = long long;

const int N = 100005;

int n, m, c, a[N], v[N];
vector<int> e[N];
priority_queue<int, vector<int>, greater<int>> p, q;
ll r;

void f(int x, int y){
    v[x] = 1;
    p.push(a[x]);
    for(int i : e[x]) if(i != y) f(i, x);
}

int main(){
    scanf("%d%d", &n, &m);
    for(int i = 0; i < n; i++) scanf("%d", a + i);
    for(int x, y; m--; ){
        scanf("%d%d", &x, &y);
        e[x].push_back(y);
        e[y].push_back(x);
    }
    for(int i = 0; i < n; i++){
        if(v[i]) continue;
        c++;
        f(i, 0);
        r += p.top();
        p.pop();
        while(!p.empty()){ q.push(p.top()); p.pop(); }
    }
    for(int i = 0; i < c - 2; i++){
        if(q.empty()){ puts("Impossible"); return 0; }
        r += q.top();
        q.pop();
    }
    printf("%lld\n", (c > 1) * r);
}