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;
typedef long long ll;

const int MAXN = 1e5+5;

ll n, m, a[MAXN], ans;
bool vis[MAXN];

vector<int> g[MAXN];
vector<int> v;
vector<int> w;

void dfs(int u) {
	vis[u] = 1;
	v.push_back(a[u]);

	for (int t : g[u])
		if (!vis[t])
			dfs(t);
}

int main() {
	cin >> n >> m;
	if (2*n-2-2*m > n) {
		cout << "Impossible\n";
		return 0;
	}
	if (m == n-1) {
		cout << 0 << endl;
		return 0;
	}

	for (int i = 0; i < n; ++i)
		cin >> a[i];

	for (int i = 0; i < m; ++i) {
		int a, b;
		cin >> a >> b;
		g[a].push_back(b);
		g[b].push_back(a);
	}

	for (int i = 0; i < n; ++i) {
		if (vis[i])
			continue;
		dfs(i);
		sort(v.begin(), v.end());
		ans += v[0];
		for (int j = 1; j < v.size(); ++j)
			w.push_back(v[j]);
		v.clear();
	}

	sort(w.begin(), w.end());
	for (int i = 0; i < n-m-2; ++i)
		ans += w[i];
	cout << ans << endl;
}