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 
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n, m;
  cin >> n >> m;
  vector<long long int> arr(0);
  for (long long int i = 0; i < n; i++) {
    long long int temp;
    cin >> temp;
    arr.push_back(temp);
  }
  sort(arr.begin(), arr.end());
  vector<long long int> arr1(0);
  vector<long long int> arr_num(0);
  for (long long int i = 0; i < n - 1; i++) {
    arr_num.push_back(arr[i + 1] - arr[i] - 1);
  }
  long long int count = m;
  long long int val = 1;
  long long int ans = 0;
  set<long long int> set_non_zero;
  for (long long int i = 0; i < n - 1; i++) {
    if (arr_num[i] > 0) {
      set_non_zero.insert(i);
    }
  }
  while (count > 0) {
    arr1.push_back(arr[0] - val);
    count -= 1;
    ans += val;
    set<long long int> set_temp;
    for (auto i = set_non_zero.begin(); i != set_non_zero.end(); i++) {
      long long int it = *i;
      if (count > 0) {
        if (arr_num[it] > 0) {
          arr1.push_back(arr[it] + val);
          count -= 1;
          arr_num[it] -= 1;
          ans += val;
          if (arr_num[it] == 0) {
            set_temp.insert(it);
          }
        }
      } else {
        break;
      }
      if (count > 0) {
        if (arr_num[it] > 0) {
          arr1.push_back(arr[it + 1] - val);
          count -= 1;
          arr_num[it] -= 1;
          ans += val;
          if (arr_num[it] == 0) {
            set_temp.insert(it);
          }
        }
      } else {
        break;
      }
    }
    for (auto j = set_temp.begin(); j != set_temp.end(); j++) {
      set_non_zero.erase(*j);
    }
    if (count > 0) {
      arr1.push_back(arr[n - 1] + val);
      count -= 1;
      ans += val;
    }
    val += 1;
  }
  cout << ans << "\n";
  for (long long int i = 0; i < m; i++) {
    cout << arr1[i] << " ";
  }
  return 0;
}
