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

n, m = map(int, stdin.readline().split())
treepos = list(map(int, stdin.readline().split()))
treepos.sort()
treespaces = []

spacecounts = {}
for i in range(n-1):
    spaces = treepos[i+1]-treepos[i]-1
    if spaces:
        spacecounts[spaces] = spacecounts.setdefault(spaces,0) + 1
        treespaces.append((spaces, treepos[i], treepos[i+1]))
treespaces.sort()
treespaces.append((-1, treepos[-1], treepos[0]))

people = []
total = 0
dist, i, c, count = 0, 0, len(treespaces), 0
while count < m:
    dist += 1
    for j in range(i,c):
        a,b = treespaces[j][1]+dist, treespaces[j][2]-dist
        people.append(a)
        if a != b:
            total+=2*dist
            people.append(b)
            count += 2
            if a+1 == b:
                i = j+1
        else:
            total+=dist
            count += 1
            i = j+1

rem = count-m
total -= dist*rem

stdout.write('{}\n'.format(total))
stdout.write(' '.join(map(str, people[0:m])))
