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 <algorithm>
#include <iostream>
#include <vector>
#define llong long long
using namespace std;

int n, m, cnt, a[100000];
llong ans;
vector<int> g[100000], e[100000], res;
bool v[100000];

void dfs(int x)
{
	v[x]=true;
	e[cnt].push_back(a[x]);

	for (int u : g[x])
		if (!v[u]) dfs(u);
}

int main()
{
	int i, j, x, y;
	cin >> n >> m;

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

	for (i=0; i<m; ++i)
	{
		cin >> x >> y;
		g[x].push_back(y);
		g[y].push_back(x);
	}

	if (n<(n-m-1)*2)
	{
		cout << "Impossible" << endl;
		return 0;
	}

	for (i=0; i<n; ++i)
		if (!v[i])
		{
			dfs(i);
			sort(e[cnt].begin(), e[cnt].end());
			ans+=(llong)e[cnt][0];

			for (j=1; j<e[cnt].size(); ++j)
				res.push_back(e[cnt][j]);

			++cnt;
		}

	if (cnt==1)
	{
		cout << '0' << endl;
		return 0;
	}

	sort(res.begin(), res.end());

	for (i=0; i<n-m-2; ++i)
		ans+=(llong)res[i];

	cout << ans << endl;
	return 0;
}