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 collections import defaultdict
n,m = list(map(int, input().split()))
As = sorted(list(map(int, input().split())))
d = defaultdict(int)
d2 = defaultdict(int)
d3 = defaultdict(int)
for a, b in zip(As, As[1:]):
    if (b + a) % 2:
        d[(b - a)//2] += 2
        d2[a] = (b-a)//2
        d3[b] = (b-a)//2
    else:
        d[(b - a)//2] += 1
        d[(b - a)//2 - 1] += 1
        d2[a] = (b-a)//2
        d3[b] = (b-a)//2-1
d[10**10] += 2
d2[As[-1]] = 10**10
d3[As[0]] = 10**10
ys = sorted(d.keys())
ly = len(As)*2
c = 0
r = 0
for i in range(m+1):
    ly -= d[i]
    if m <= c + ly:
        r += (i+1)*(m-c)
        v = m-c
        break
    c += ly
    r += (i+1)*ly
rs = set()
for a in As:
    if d2[a] > i and v > 0:
        kk = i+1
        v-=1
    else:
        kk = min(d2[a], i)
    for j in range(1, kk+1):
        rs.add(a+j)
    if d3[a] > i and v > 0:
        kk = i+1
        v-=1
    else:
        kk = min(d3[a], i)
        #print(d3)
        #print(a, d3[a], i)
    for j in range(1, kk+1):
        #print(a, a-j)
        rs.add(a-j)
print(r)
print(*list(rs))
