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 
n,m=[int(x) for x in input().split()]
a=list(sorted([int(x) for x in input().split()]))
b=[a[i]-a[i-1]-1 for i in range(1,n)]
c=set()
for i in range(n-1):
    if b[i]!=0:
        c.add(i)
res=[]
su=0
x=1
while m!=0:
    if m>2:
        res.extend([a[0]-x,a[-1]+x])
        su+=2*x
        m-=2
        tmp=set()
        for i in c:
            if m>1:
                if b[i]>2:
                    m-=2
                    b[i]-=2
                    su+=2*x
                    tmp.add(i)
                    res.extend([a[i]+x,a[i+1]-x])
                elif b[i]==2:
                    m-=2
                    su+=2*x
                    b[i]=0
                    res.extend([a[i]+x,a[i+1]-x])
                else:
                    m-=1
                    su+=x
                    b[i]=0
                    res.append(a[i]+x)
            else:
                m=0
                res.append(a[i]+x)
                su+=x
            if m==0:
                break
        if m==0:
            continue
        c=tmp|set()
    elif m==2:
        res.extend([a[0]-x,a[-1]+x])
        m=0
        su+=2*x
    else:
        res.append(a[0]-x)
        m=0
        su+=x
    x+=1
print(su)
print(*res)
