#include <bits/stdc++.h>
using namespace std;
int main() {
  int n, m;
  cin >> n >> m;
  int tempm = m;
  int a[n];
  set<int> tree, human, st;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    tree.insert(a[i]);
    st.insert(a[i]);
  }
  long long res = 0;
  int j = 1;
  while (m > 0) {
    set<int> temp;
    for (int e : st) {
      bool t1 = 0, t2 = 0;
      if (m > 0 && tree.find(e + j) == tree.end() &&
          human.find(e + j) == human.end()) {
        res += j;
        human.insert(e + j);
        m--;
        t1 = 1;
      }
      if (m > 0 && tree.find(e - j) == tree.end() &&
          human.find(e - j) == human.end()) {
        res += j;
        human.insert(e - j);
        m--;
        t2 = 1;
      }
      if (m <= 0) break;
      if (t1 || t2) temp.insert(e);
    }
    st = temp;
    j++;
  }
  cout << res << endl;
  for (int e : human) cout << e << " ";
}

### Prompt

Please create a solution in CPP 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;
int main() {
  int n, m;
  cin >> n >> m;
  int tempm = m;
  int a[n];
  set<int> tree, human, st;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    tree.insert(a[i]);
    st.insert(a[i]);
  }
  long long res = 0;
  int j = 1;
  while (m > 0) {
    set<int> temp;
    for (int e : st) {
      bool t1 = 0, t2 = 0;
      if (m > 0 && tree.find(e + j) == tree.end() &&
          human.find(e + j) == human.end()) {
        res += j;
        human.insert(e + j);
        m--;
        t1 = 1;
      }
      if (m > 0 && tree.find(e - j) == tree.end() &&
          human.find(e - j) == human.end()) {
        res += j;
        human.insert(e - j);
        m--;
        t2 = 1;
      }
      if (m <= 0) break;
      if (t1 || t2) temp.insert(e);
    }
    st = temp;
    j++;
  }
  cout << res << endl;
  for (int e : human) cout << e << " ";
}

```