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 
import string
from collections import defaultdict,Counter
from math import sqrt, log10, log2, log, gcd, ceil, floor,factorial
from bisect import bisect_left, bisect_right
from itertools import permutations,combinations_with_replacement
import sys,io,os;
input=sys.stdin.readline
# input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
# print=sys.stdout.write
sys.setrecursionlimit(10000)
mod=int(pow(10,7)+9)
inf = float('inf')
def get_list():
    return [int(i) for i in input().split()]
def yn(a):
    print("YES" if a else "NO",flush=False)
t=1

for i in range(t):
    n,m=get_list()
    y=get_list()

    yset=set(y)
    occupied=set(y)
    res=0

    dist=1;
    newlist=y;
    while len(occupied)<n+m:
        traverse=newlist
        newlist=[]
        for j in traverse:
            prevres=res;
            if j-dist not in occupied:
                occupied.add(j-dist)
                res+=dist
            if len(occupied)==n+m:
                break;
            if j+dist not in occupied:
                occupied.add(j+dist)
                res+=dist;
            if len(occupied)==n+m:
                break;
            if prevres!=res:
                newlist.append(j)
        dist+=1
    answer=[i for i in occupied if i not in yset]
    print(res)
    print(*answer)








