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 <iostream>
#include <cstdio>
#include <algorithm>
#include <vector>
#define N 100005
using namespace std;
typedef long long ll;

ll n, m, ans, gr, a[N], pr[N];
vector<ll> fr[N], all;

ll fnd(ll p) {
	if(pr[p]==p) return p;
	return pr[p] = fnd(pr[p]);
}

int main() {
	ll i, j, x, y;
	cin >> n >> m;
	for(i=0; i<n; i++) {
		scanf("%lld", &a[i]);
		pr[i] = i;
	}
	for(i=0; i<m; i++) {
		scanf("%lld%lld", &x, &y);
		x = fnd(x);
		y = fnd(y);
		pr[x] = y;
	}
	for(i=0; i<n; i++) fr[fnd(i)].push_back(a[i]);
	for(i=0; i<n; i++) {
		if(fr[i].empty()) continue;
		gr++;
		sort(fr[i].begin(), fr[i].end());
		ans += fr[i][0];
		for(j=1; j<fr[i].size(); j++) all.push_back(fr[i][j]);
	}
	if(gr==1) return puts("0")*0;
	if((int)all.size() < 2*(n-m-1)-gr) return puts("Impossible")*0;
	sort(all.begin(), all.end());
	for(i=0; i<2*(n-m-1)-gr; i++) ans += all[i];
	cout << ans;
	return 0;
}