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 nm = 1e5;
int n, m, a[nm], tn = 0;
vector<int> g[nm];
bool b[nm];

priority_queue<int, vector<int>> q;

int minDfs(int v, int p) {

	b[v] = 1;
	int rv = a[v];
	for (int nv : g[v]) {
		if (nv == p)
			continue;
		int minNext = minDfs(nv, v);
		if (minNext < rv)
			swap(rv, minNext);
		q.push(minNext);
		if ((int) q.size() > n - m - 2)
			q.pop();
	}
	return rv;
}
long long ans = 0;

int main() {
	cin >> n >> m;
	if (m == n - 1) {
		cout << 0 << endl;
		return 0;
	}
	if ((n - m - 1) * 2 > n) {
		cout << "Impossible" << endl;
		return 0;
	}
	for (int i = 0; i < n; i++)
		cin >> a[i];
	for (int i = 0, x, y; i < m; i++) {
		cin >> x >> y;
		g[x].push_back(y);
		g[y].push_back(x);
	}
	for (int i = 0; i < n; i++) {
		if (!b[i])
			ans += minDfs(i, -1);
	}
	while (!q.empty()) {
		ans += q.top();
		q.pop();
	}
	cout << ans << endl;
}
