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;
vector<string> v(2);
int inf = 1e+9;
int flag = 0;
vector<int> lvl;
int n, m;
vector<string> vec;
int tx, ty, sx, sy;
vector<vector<vector<int> > > d;
struct str {
  long long val, pos, limit, opr;
};
struct comp {
  bool operator()(str &s1, str &s2) { return s1.val > s2.val; }
};
int main() {
  long long n, m;
  cin >> n >> m;
  priority_queue<str, vector<str>, comp> pq;
  vector<long long> v(n);
  for (int i = 0; i < n; i++) cin >> v[i];
  sort(v.begin(), v.end());
  pq.push({1, v[0], 1000000000, -1});
  pq.push({1, v[n - 1], 1000000000, 1});
  for (int i = 1; i < n; i++) {
    long long x = v[i] - v[i - 1];
    if (x == 0) continue;
    if (x / 2 > 0) pq.push({1, v[i - 1], x / 2, 1});
    if (x - 1 - x / 2 > 0) pq.push({1, v[i], x - x / 2 - 1, -1});
  }
  vector<long long> ans;
  long long count = 0;
  for (int i = 0; i < m; i++) {
    str t = pq.top();
    pq.pop();
    if (t.val < t.limit) {
      pq.push({t.val + 1, t.pos, t.limit, t.opr});
    }
    count += t.val;
    ans.push_back(t.val * t.opr + t.pos);
  }
  cout << count << endl;
  for (auto i : ans) cout << i << " ";
  cout << endl;
}
