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 w[100005],d[100005],z[100005];
int f(int x){ return d[x]==x?x:d[x]=f(d[x]); }

priority_queue<int,vector<int>,greater<int>> pq[100005];

int main(){
    int n,m; cin>>n>>m;
    for(int i=1;i<=n;++i)cin>>w[i];
    for(int i=1;i<=n;++i)d[i]=i;
    while(m--){
        int u,v; cin>>u>>v; ++u, ++v;
        d[f(u)]=f(v);
    }
    for(int i=1;i<=n;++i)pq[f(i)].push(w[i]);
    for(int i=1;i<=n;++i)z[i]=i;
    sort(z+1,z+1+n,[&](const int &a,const int &b){ return pq[a].size()>pq[b].size(); });
    long long ans=0;
    for(int x=2;x<=n;++x){
        int i=z[x];
        if(pq[i].size() && !pq[z[1]].size())exit((cout<<"Impossible"<<endl,0));
        if(pq[i].empty())continue;
        ans+=pq[i].top()+pq[z[1]].top();
        pq[i].pop(); pq[z[1]].pop();
        while(pq[i].size()){ pq[z[1]].push(pq[i].top()); pq[i].pop(); }
    }
    cout<<ans<<endl;
}
