#include <bits/stdc++.h>
using namespace std;
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n, k, x, s = 0;
  cin >> n >> k;
  map<long long, long long> m;
  queue<long long> q;
  for (long long i = 0; 0 < n ? i < n : i > n; 0 < n ? i += 1 : i -= 1) {
    cin >> x;
    q.push(x);
    m[x] = 0;
  }
  while (1) {
    x = q.front();
    q.pop();
    if (!m.count(x + 1)) {
      q.push(x + 1);
      m[x + 1] = m[x] + 1;
    }
    if (m.size() >= n + k) break;
    if (!m.count(x - 1)) {
      q.push(x - 1);
      m[x - 1] = m[x] + 1;
    }
    if (m.size() >= n + k) break;
  }
  for (auto i : m) s += i.second;
  cout << s << "\n";
  for (auto i : m)
    if (i.second != 0) cout << i.first << " ";
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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;
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n, k, x, s = 0;
  cin >> n >> k;
  map<long long, long long> m;
  queue<long long> q;
  for (long long i = 0; 0 < n ? i < n : i > n; 0 < n ? i += 1 : i -= 1) {
    cin >> x;
    q.push(x);
    m[x] = 0;
  }
  while (1) {
    x = q.front();
    q.pop();
    if (!m.count(x + 1)) {
      q.push(x + 1);
      m[x + 1] = m[x] + 1;
    }
    if (m.size() >= n + k) break;
    if (!m.count(x - 1)) {
      q.push(x - 1);
      m[x - 1] = m[x] + 1;
    }
    if (m.size() >= n + k) break;
  }
  for (auto i : m) s += i.second;
  cout << s << "\n";
  for (auto i : m)
    if (i.second != 0) cout << i.first << " ";
}

```