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;
int par[100001];
bool v[100001];
int root(int x){
	if(par[x]==x) return x;
	return par[x]=root(par[x]);
}
int main(){
	int N,M,x,y,X,Y,rx,ry;
	long long c=0;
	scanf("%d%d",&N,&M);
	int n=2*(N-M-1);
	multiset<int> b;
	if(M==N-1)
		printf("0");
	else if(n>N)
		printf("Impossible");
	else{
		long long fre[N];
		long long a[N];
		for(int i=0;i<N;i++){
			scanf("%lld",&a[i]);
			par[i]=i;
			fre[i]=a[i];
		}

		for(int i=0;i<M;i++){
			scanf("%d%d",&x,&y);
			rx=root(x);
			ry=root(y);
			if(fre[ry]<fre[rx]){
			fre[rx]=fre[ry];
			par[rx]=ry;
			}else{
			fre[ry]=fre[rx];
			par[ry]=rx;
			}
		}
		for(int i=0;i<N;i++){
			rx=root(i);
			if(!v[rx]){
				c+=a[rx];
				n--;
				v[rx]=1;
			}
			if (!v[i]){
				b.insert(a[i]);
			}
		}
		while(n--){
			c+=*b.begin();
			b.erase(b.begin());
		}
		printf("%lld",c);
	}
}
