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;

const int N = 100005;
multiset<int> ms[N];

vector<int> con[N];
int comp;
int a[N];
bool vis[N];
void dfs(int s){
	ms[comp].insert(a[s]);
	vis[s] = 1;
	for(int v : con[s]) if(!vis[v]) dfs(v);
}

vector<int> vec;
int main(){
	int n, m;
	cin >> n >> m;
	for(int i = 1; i <= n; i++) cin >> a[i];
	for(int i = 1; i <= m; i++){
		int u, v;
		cin >> u >> v;
		u++; v++;
		con[u].push_back(v);
		con[v].push_back(u);
	}
	long long ans = 0;
	for(int i = 1; i <= n; i++){
		if(!vis[i]){
			comp++;
			dfs(i);
			ans += *ms[comp].begin();
			ms[comp].erase(ms[comp].begin());
			for(int x : ms[comp]) vec.push_back(x);
		}
	}
	if(comp == 1){
		printf("0\n");
		return 0;
	}

	sort(vec.begin(), vec.end());
	int req = comp - 2;
	if(vec.size() < req){
		printf("Impossible\n");
		return 0;
	}
	for(int i = 0; i < req; i++) ans += vec[i];
	printf("%lld\n", ans);
}
