Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

7 5
1 2 3 4 5 6 7
3 0
4 0
1 2
1 3
5 6

Sample Output 1

7

If we connect vertices 0 and 5, the graph becomes connected, for the cost of 1 + 6 = 7 dollars.

Sample Input 2

5 0
3 1 4 1 5

Sample Output 2

Impossible

We can't make the graph connected.

Sample Input 3

1 0
5

Sample Output 3

0

The graph is already connected, so we do not need to add any edges.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

/**
*/
#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int maxn=1e5+5;
int N,M;
struct node{int id,v;} a[maxn],minn[maxn];
int fa[maxn];
bool vis[maxn];

int findfa(int x){
	return x==fa[x]?x:fa[x]=findfa(fa[x]);
}
bool cmp(node &a,node &b){
	return a.v<b.v;
}
int main()
{
#ifdef _WY
freopen("0905.in","r",stdin);
#endif // _WY

	scanf("%d%d",&N,&M);
	for(int i=0;i<N;++i){
		scanf("%d",&a[i].v);
		a[i].id=i;
		fa[i]=i;
		minn[i].v=a[i].v;
		minn[i].id=i;
	}

	int u,v;
	for(int i=0;i<M;++i){
		scanf("%d%d",&u,&v);
		int fu=findfa(u);
		int fv=findfa(v);
		if(fu!=fv) fa[fu]=fv;
	}

	LL ans=0;
	for(int i=0;i<N;++i){
		int fi=findfa(i);
		if(minn[fi].v>a[i].v){
			minn[fi].v=a[i].v;
			minn[fi].id=i;
		}
	}

	int cnt=0;
	for(int i=0;i<N;++i){
		if(i==findfa(i)) {
			cnt++;
			ans+=minn[i].v;
			vis[minn[i].id]=true;
		}
	}

	if(N<2*(cnt-1)){
		puts("Impossible");
		return 0;
	}
	if(N==1){
		puts("0");
		return 0;
	}
	sort(a,a+N,cmp);int j=0;
	for(int i=0;i<cnt-2;++j){
		if(!vis[a[j].id]){
			ans+=a[j].v;
			i++;
		}
	}

	printf("%lld\n",ans);
	return 0;
}