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 
from sys import stdin, stdout
from heapq import heappush, heappop

def main():
    arr = list(map(int, stdin.readline().split()))
    tree = list(map(int, stdin.readline().split()))
    tree.sort()
    people = arr[1]
    heaper = []
    standing_list = list()
    cost = 0
    done = 0
    smallest = 0
    for i,x in enumerate(tree):
        if i == 0:
            continue
        heappush(heaper, (tree[i] - tree[i - 1] - 1, tree[i-1], tree[i]))
    while done < people:
        smallest += 1
        while heaper and heaper[0][1] + smallest >= heaper[0][2] - smallest:
            temp_pop = heappop(heaper)
            if temp_pop[1] + smallest == temp_pop[2] - smallest:
                done +=1
                cost += smallest
                standing_list.append(temp_pop[1] + smallest)
                if done >= people:
                    break
        if done >= people:
            break
        if len(heaper) > 0:
            for x in heaper:
                done += 2
                cost += smallest*2
                standing_list.append(x[1] + smallest)
                standing_list.append(x[2] - smallest)
                if done >= people:
                    break
        if done >= people:
            break
        standing_list.append(tree[0] - smallest)
        done +=1
        cost += smallest
        standing_list.append(tree[-1] + smallest)
        done +=1
        cost += smallest
    while done > people:
        cost -= smallest
        del standing_list[-1]
        done -= 1
    stdout.write(str(cost)+"\n")
    stdout.write(' '.join(map(str, standing_list)))
    
main()