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 vi = std::vector<int>;
std::priority_queue<int, std::vector<int>, std::greater<int>> pq;

vi a;
std::vector<vi> edges;
std::vector<bool> used;

int dfs(int);
int64_t solve();

int main()
{
	int64_t ans{solve()};
	if (ans < 0) puts("Impossible");
	else printf("%lld\n", ans);

	return 0;
}

int64_t solve()
{
	int N, M;
	scanf("%d%d", &N, &M);
	a.resize(N);
	for (int i{}; i < N; i++)
		scanf("%d", &a[i]);
	edges.resize(N);
	for (int i{}; i < M; i++)
	{
		int x, y;
		scanf("%d%d", &x, &y);
		edges[x].push_back(y);
		edges[y].push_back(x);
	}
	if (M + N / 2 < N - 1) return -1;
	used.resize(N);
	int64_t sum{};
	for (int i{}; i < N; i++)
	{
		if (used[i]) continue;
		int min_i{dfs(i)};
		sum += a[min_i];
	}
	if (M == N - 1) sum = 0;
	for (int i{}; i < N - 1 - M - 1; i++)
	{
		sum += pq.top();
		pq.pop();
	}
	return sum;
}

int dfs(int index)
{
	used[index] = true;
	int min_i{index};
	for (auto& e: edges[index])
	{
		if (used[e]) continue;
		int tmp{dfs(e)};
		if (a[tmp] < a[min_i]) std::swap(tmp, min_i);
		pq.push(a[tmp]);
	}
	return min_i;
}