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 math
import time
from collections import defaultdict,deque
from sys import stdin,stdout
from bisect import bisect_left,bisect_right
from queue import PriorityQueue 
import sys
class Graph:
    def __init__(self, n):
        self.graph = defaultdict(lambda: [])
        self.vertices = n
        self.toposorted = []

    def addEdge(self, a, b):  # tested
        self.graph[a].append(b)

    def cycleUntill(self, visited, curr, parent):  # tested
        visited[curr] = True
        for i in self.graph[curr]:
            if(not visited[i]):
                if(self.cycleUntill(visited, i, curr)):
                    return True
            elif(i != parent):
                return True
        return False

    def cycle(self):  # tested
        n = self.vertices
        visited = [False]*(n+2)
        for i in range(1, n+1):
            if(not visited[i]):
                if(self.cycleUntill(visited, i, -1)):
                    return True
        return False

    def topologicalSort(self):#tested
        in_degree = [0]*(self.vertices+10)
        for i in self.graph:
            for j in self.graph[i]:
                in_degree[j] += 1
        queue = deque()
        for i in range(1,self.vertices+1):
            if in_degree[i] == 0:
                queue.append(i)
        cnt = 0
        while queue:
            u = queue.popleft()
            self.toposorted.append(u)
            for i in self.graph[u]:
                in_degree[i] -= 1
                if in_degree[i] == 0:
                    queue.append(i)
            cnt += 1
        if cnt != self.vertices:
            return False
        else:
            return True

n,m=map(int,stdin.readline().split())
a=list(map(int,stdin.readline().split()))
dist=defaultdict(lambda:0)
q=deque()
done=set()
for i in a:
    q.append(i)
    done.add(i)
ans=[]
val=0
while(len(q)>0):
    if(len(ans)==m):
        break
    temp=q.popleft()
    if(dist[temp]!=0):
        val+=dist[temp]
        ans.append(temp)
    if(temp-1 not in done):
        dist[temp-1]=dist[temp]+1
        q.append(temp-1)
        done.add(temp-1)
    if(temp+1 not in done):
        dist[temp+1]=dist[temp]+1
        q.append(temp+1)
        done.add(temp+1)
print(val)
print(*ans)
    

