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 
# -*- coding: utf-8 -*-

import sys
import heapq

def read_int_list():
    return map(int, sys.stdin.readline().strip().split())

def read_int():
    return int(sys.stdin.readline().strip())


def solve():
    trees_cnt, people_cnt = read_int_list()
    trees_coords = read_int_list()
    heap = []
    busy = set()
    for tc in trees_coords:
        busy.add(tc)

    for tc in trees_coords:
        if tc-1 not in busy:
            heapq.heappush(heap, (1, [tc, tc-1]))  # distance + [tree coord, empty space]
        if tc+1 not in busy:
            heapq.heappush(heap, (1, [tc, tc+1]))
    # print(heap)

    r = 0
    people_coords = []
    for _ in xrange(people_cnt):
        while True:
            v = heapq.heappop(heap)
            distance, [tree_coord, empty_coord] = v
            if empty_coord not in busy:
                r += distance
                busy.add(empty_coord)
                people_coords.append(str(empty_coord))
                break

        if empty_coord < tree_coord:
            # left
            if empty_coord - 1 not in busy:
                heapq.heappush(heap, (distance+1, [tree_coord, empty_coord - 1]))
        else:
            # right
            if empty_coord + 1 not in busy:
                heapq.heappush(heap, (distance+1, [tree_coord, empty_coord + 1]))

    sys.stdout.write('%s\n' % r)
    sys.stdout.write(' '.join(people_coords) + '\n')
    # print('result', sorted(map(int, people_coords)))


solve()
