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 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#define inf 2e30+1
typedef long long ll;

int compare(const void *a, const void *b) {
  return *(int*)a - *(int*)b;
}

int main(void) {
  int i, j, k, n, m;
  scanf("%d%d", &n, &m);
  int x, y, uni[n], a[n];
  for(i = 0; i < n; ++i) scanf("%d", &a[i]);
  for(i = 0; i < n; ++i) uni[i] = i;
  for(i = 0; i < m; ++i) {
    scanf("%d%d", &x, &y);
    int t;
    if(uni[x] != x) {
      t = uni[y];
      uni[y] = x;
      for(j = y; uni[j] != j; ) {
        j = uni[j];
      }
      uni[y] = j;
      for(j = 0; j < n; ++j) {
        if(j == y) continue;
        if(uni[j] == t) uni[j] = uni[y];
      }
    } else {
      t = uni[x];
      uni[x] = y;
      for(j = x; uni[j] != j; ) {
        j = uni[j];
      }
      uni[x] = j;
      for(j = 0; j < n; ++j) {
        if(j == x) continue;
        if(uni[j] == t) uni[j] = uni[x];
      }
    }
  /*for(j = 0; j < n; ++j) printf("%d ", uni[j]);
  printf("\n");*/
  }
  int num = 0;
  for(i = 0; i < n; ++i) {
    if(uni[i] == i) ++num;
  }
  if(num == 1) {
    printf("0");
    return 0;
  }
  if(num * 2 - 2 > n) {
    printf("Impossible");
    return 0;
  }
  if(num * 2 - 2 == n) {
    int t = 0;
    for(i = 0; i < n; ++i) t += a[i];
    printf("%d", t);
    return 0;
  }
  int min[n], minn[n];
  for(i = 0; i < n; ++i) min[i] = inf;
  for(i = 0; i < n; ++i) if(min[uni[i]] > a[i]) min[uni[i]] = a[i], minn[uni[i]] = i;
  ll ssum = 0;
  int tnum = num - 2;
  //return 0;
  //for(i = 0; i < n; ++i) printf("%d ", min[i]);
  //printf("%d", inf);
  for(i = 0; i < n; ++i) {
    int y = inf;
    if(min[i] != y) {
      ssum += (ll)min[i];
      a[minn[i]] = inf;
    }
  }
  qsort(a, n, sizeof(int), compare);
  //return 0;
  for(i = 0; i < tnum; ++i) {
    ssum += a[i];
  }
  printf("%lld", ssum);
  return 0;
}