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 sys
LI=lambda:list(map(int, sys.stdin.readline().strip('\n').split()))
MI=lambda:map(int, sys.stdin.readline().strip('\n').split())
SI=lambda:sys.stdin.readline().strip('\n')
II=lambda:int(sys.stdin.readline().strip('\n'))

n, m=MI()
a=sorted(LI())
taken=set(a)
q=a.copy()
i, cnt=0, 0
while cnt<m:
	u=q[i]
	if u-1 not in taken:
		taken.add(u-1)
		q.append(u-1)
		cnt+=1
	if cnt>=m:
		break
	if u+1 not in taken:
		taken.add(u+1)
		q.append(u+1)
		cnt+=1
	i+=1
ans=taken.difference(set(a))
val=0
for v in ans:
	l, r=0, n-1
	v1, v2=-1, -1
	while l<=r:
		m=(l+r)//2
		if a[m]<=v:
			v1=m
			l=m+1
		else:
			r=m-1
	l, r=0, n-1
	while l<=r:
		m=(l+r)//2
		if a[m]<v:
			l=m+1
		else:
			v2=m
			r=m-1
	if v1!=-1 and v2!=-1:
		val+=min(abs(v-a[v1]), abs(v-a[v2]))
	elif v1!=-1:
		val+=abs(v-a[v1])
	else:
		val+=abs(v-a[v2])
print(val)
print(*ans)