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 
def oneLineArrayPrint(arr):
    print(' '.join([str(x) for x in arr]))

from queue import deque

n,m=[int(x) for x in input().split()]
a=[int(z) for z in input().split()]

occupiedPositions=set()

for x in a:
    occupiedPositions.add(x) #all trees

ans=[]
positionQ=deque() #store [position,distance from nearest XMas Tree]

a.sort()
for i in range(n):
    if a[i]-1 not in occupiedPositions: #all space on the left and right of trees (if not already occupied)
        positionQ.append([a[i]-1,1])
        occupiedPositions.add(a[i]-1)
    if a[i]+1 not in occupiedPositions:
        positionQ.append([a[i]+1,1])
        occupiedPositions.add(a[i]+1)
totalDistance=0
while len(ans)<m:
    pos,dis=positionQ.popleft()
    totalDistance+=dis
    ans.append(pos)
    if pos-1 not in occupiedPositions:
        occupiedPositions.add(pos-1)
        positionQ.append([pos-1,dis+1])
    if pos+1 not in occupiedPositions:
        occupiedPositions.add(pos+1)
        positionQ.append([pos+1,dis+1])
#    print('pos:{} occupied:{} queue:{}'.format(pos,occupiedPositions,positionQ))

print(totalDistance)
oneLineArrayPrint(ans)