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=map(int,input().split())
a=list(map(int,input().split()))
d={}
a.sort()

low=1
high=m

for i in a:
    d[i]=2

from collections import deque

def check(mid,a):
    s=0
    for i in range(n-1):
        s+=min(2*mid,a[i+1]-a[i]-1)
    if s+ 2*mid>=m:
        return True
    else:
        return False
        
    

while low<high:
    mid=(low+high)//2
    if check(mid,a):
        high=mid
    else:
        low=mid+1

st=deque(a)
# print(st)
k=0
ans=[]
pr=0
while m>0:
    if st[0]==a[0]:
        k+=1
        
    if st[0]-k  in d and st[0]+k in d:
        st.popleft()
        continue
    # print(ans)
    if st[0]-k  not in d:
        d[st[0]-k]=1
        m-=1
        pr+=k
        ans.append(st[0]-k)
    # print(ans)    
    if st[0]+k  not in d and m>0:
        d[st[0]+k]=1
        m-=1
        pr+=k
        ans.append(st[0]+k)
    # print(ans)    
    st.append(st.popleft())
    
print(pr)    
print(*ans)        