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;
const long long N = 200000 + 10;
long long n, m, w[N], st[N], ans;
set<int> p;
struct node {
  long long bh, dis, wei;
  bool operator<(const node a) const { return a.dis < dis; }
} t, base;
priority_queue<node> pls;
int main() {
  scanf("%lld%lld", &n, &m);
  for (int i = 1; i <= n; i++) {
    scanf("%lld", &w[i]);
    p.insert(w[i]);
  }
  for (int i = 1; i <= n; i++) {
    if (!p.count(w[i] - 1)) {
      base.bh = i;
      base.dis = 1;
      base.wei = w[i] - 1;
      pls.push(base);
      p.insert(w[i] - 1);
    }
    if (!p.count(w[i] + 1)) {
      base.bh = i;
      base.dis = 1;
      base.wei = w[i] + 1;
      pls.push(base);
      p.insert(w[i] + 1);
    }
  }
  for (int i = 1; i <= m; i++) {
    t = pls.top();
    pls.pop();
    st[i] = t.wei;
    ans += t.dis;
    if (!p.count(w[t.bh] - (t.dis + 1))) {
      base.bh = t.bh;
      base.dis = t.dis + 1;
      base.wei = w[t.bh] - (t.dis + 1);
      pls.push(base);
      p.insert(w[t.bh] - (t.dis + 1));
    }
    if (!p.count(w[t.bh] + (t.dis + 1))) {
      base.bh = t.bh;
      base.dis = t.dis + 1;
      base.wei = w[t.bh] + (t.dis + 1);
      pls.push(base);
      p.insert(w[t.bh] + (t.dis + 1));
    }
  }
  printf("%lld\n", ans);
  for (int i = 1; i <= m; i++) printf("%lld ", st[i]);
  return 0;
}
