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 collections import deque


def solve():

    input_str = input().split()
    n = int(input_str[0])
    m = int(input_str[1])

    pos = input().split()

    seen = set([int(x) for x in pos])
    queue = deque([int(x) for x in pos])

    total_dist = 0
    cur_dist = 0
    ans = []
    exitf = False
    while queue:

        for i in range(len(queue)):
            cur = queue.popleft()

            if (cur_dist > 0):
                total_dist += cur_dist

                ans.append(cur)

                if len(ans) == m:
                    exitf = True
                    break

            if cur - 1 not in seen:
                seen.add(cur - 1)
                queue.append(cur - 1)

            if cur + 1 not in seen:
                seen.add(cur + 1)
                queue.append(cur + 1)


        cur_dist += 1

        if exitf == True:
            break

    print(total_dist)

    for i in range(m):
        print(ans[i], end=" ")
    
    return 0


solve()