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 atexit
import io
import sys
import heapq
_INPUT_LINES = sys.stdin.read().splitlines()
raw_input = iter(_INPUT_LINES).next
_OUTPUT_BUFFER = io.BytesIO()
sys.stdout = _OUTPUT_BUFFER

@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
    
def takla():
    
    
    n,m=map(int,raw_input().split())
    x=[int(o) for o in raw_input().split()]
    c=0
    i=1
    j=1
    k=0
    s=set(x)
    h=[]
    ans=[]
    for i in range(n):
        if x[i]-1 not in s:
            heapq.heappush(h,[1,-1,x[i]-1])
            
        if x[i]+1 not in s:
            heapq.heappush(h,[1,1,x[i]+1])
    while c!=m:
        lol=heapq.heappop(h)
        if lol[1]>0:
            if lol[2] not in s:
                s.add(lol[2])
                ans.append(lol[2])
                c+=1
                k+=lol[0]
                lol[1]+=1
                lol[0]+=1
                lol[2]+=1
                # c+=1
                if lol[2] not in s:
                    heapq.heappush(h,lol[:])
                    # c+=1
        else:
            if lol[2] not in s:
                s.add(lol[2])
                ans.append(lol[2])
                c+=1
                k+=lol[0]
                lol[1]-=1
                lol[0]+=1
                lol[2]-=1
                # c+=1
                if lol[2] not in s:
                    heapq.heappush(h,lol[:])
     
    print(k)
    for i in xrange(m):
        print ans[i],
          
    
if __name__ == "__main__":
	takla()