#include <bits/stdc++.h>
using namespace std;
map<int, int> mp;
int main() {
  int n, m;
  cin >> n >> m;
  set<int> s, t;
  int aa;
  for (int i = 0; i < n; i++) {
    cin >> aa;
    mp[aa]++;
    s.insert(aa);
  }
  long long l = 1, c;
  long long ans = 0;
  while (t.size() < m) {
    auto i = s.begin();
    while (i != s.end()) {
      c = 0;
      auto tt = *i;
      if (!mp[*i + l] && t.find(*i + l) == t.end()) {
        c++;
        t.insert(*i + l);
        ans += l;
      }
      if (t.size() >= m) break;
      if (!mp[*i - l] && t.find(*i - l) == t.end()) {
        t.insert(*i - l);
        c++;
        ans += l;
      }
      if (t.size() >= m) break;
      i++;
      if (!c) {
        s.erase(tt);
      }
    }
    l++;
  }
  cout << ans << endl;
  for (auto i = t.begin(); i != t.end(); i++) cout << *i << " ";
}

### Prompt

Generate a cpp solution to the following problem:

There are n Christmas trees on an infinite number line. The i-th tree grows at the position x_i. All x_i are guaranteed to be distinct.

Each integer point can be either occupied by the Christmas tree, by the human or not occupied at all. Non-integer points cannot be occupied by anything.

There are m people who want to celebrate Christmas. Let y_1, y_2, ..., y_m be the positions of people (note that all values x_1, x_2, ..., x_n, y_1, y_2, ..., y_m should be distinct and all y_j should be integer). You want to find such an arrangement of people that the value ∑_{j=1}^{m}min_{i=1}^{n}|x_i - y_j| is the minimum possible (in other words, the sum of distances to the nearest Christmas tree for all people should be minimized).

In other words, let d_j be the distance from the j-th human to the nearest Christmas tree (d_j = min_{i=1}^{n} |y_j - x_i|). Then you need to choose such positions y_1, y_2, ..., y_m that ∑_{j=1}^{m} d_j is the minimum possible.

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 2 ⋅ 10^5) — the number of Christmas trees and the number of people.

The second line of the input contains n integers x_1, x_2, ..., x_n (-10^9 ≤ x_i ≤ 10^9), where x_i is the position of the i-th Christmas tree. It is guaranteed that all x_i are distinct.

Output

In the first line print one integer res — the minimum possible value of ∑_{j=1}^{m}min_{i=1}^{n}|x_i - y_j| (in other words, the sum of distances to the nearest Christmas tree for all people).

In the second line print m integers y_1, y_2, ..., y_m (-2 ⋅ 10^9 ≤ y_j ≤ 2 ⋅ 10^9), where y_j is the position of the j-th human. All y_j should be distinct and all values x_1, x_2, ..., x_n, y_1, y_2, ..., y_m should be distinct.

If there are multiple answers, print any of them.

Examples

Input


2 6
1 5


Output


8
-1 2 6 4 0 3 


Input


3 5
0 3 1


Output


7
5 -2 4 -1 2 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
map<int, int> mp;
int main() {
  int n, m;
  cin >> n >> m;
  set<int> s, t;
  int aa;
  for (int i = 0; i < n; i++) {
    cin >> aa;
    mp[aa]++;
    s.insert(aa);
  }
  long long l = 1, c;
  long long ans = 0;
  while (t.size() < m) {
    auto i = s.begin();
    while (i != s.end()) {
      c = 0;
      auto tt = *i;
      if (!mp[*i + l] && t.find(*i + l) == t.end()) {
        c++;
        t.insert(*i + l);
        ans += l;
      }
      if (t.size() >= m) break;
      if (!mp[*i - l] && t.find(*i - l) == t.end()) {
        t.insert(*i - l);
        c++;
        ans += l;
      }
      if (t.size() >= m) break;
      i++;
      if (!c) {
        s.erase(tt);
      }
    }
    l++;
  }
  cout << ans << endl;
  for (auto i = t.begin(); i != t.end(); i++) cout << *i << " ";
}

```