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 
from sys import stdin
raw_input = lambda: stdin.readline().rstrip()
input = lambda: int(raw_input())
I=lambda: map(int, raw_input().split())
n,m = I()
a = I()
a.sort()
qm = a[0]
qM = a[n-1]
lst = []
for i in xrange(1, n):
	d = a[i]-a[i-1]
	if d > 1:
		lst.append((a[i-1], a[i], d-1))
lst.sort(key=lambda x:x[2])
lLst = len(lst)
curI = 0
curD = 1
rLst = []
r = 0
while m>0:
	r += curD
	rLst.append(str(qm-curD))
	m -= 1
	if m==0:
		break
	r += curD
	rLst.append(str(qM+curD))
	m -= 1
	if m==0:
		break
	for i in xrange(curI, lLst):
		a1, b1, d = lst[i]
		if d==1:
			r += curD
			rLst.append(str(a1+1))
			m -= 1
			if m==0:
				break
			curI += 1
		elif d==2:
			r += curD
			rLst.append(str(a1+1))
			m -= 1
			if m==0:
				break
			r += curD
			rLst.append(str(a1+2))
			m -= 1
			if m==0:
				break
			curI += 1
		else:
			r += curD
			rLst.append(str(a1+1))
			m -= 1
			if m==0:
				break
			r += curD
			rLst.append(str(b1-1))
			m -= 1
			if m==0:
				break
			lst[i] = (a1+1, b1-1, d-2)
	curD += 1
	if m == 0:
		break
print r
print ' '.join(rLst)