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 
def main():
    class node:
      def __init__(self,val):
        self.val = val
        self.next = None
    n,m = map(int,input().strip().split())
    A = sorted(list(map(int,input().strip().split())))
    sa = set(A)
    L = [node(A[i]) for i in range(n)]
    for i in range(n-1):
        L[i].next = L[i+1]

    p = set()
    x = 0
    flag=0
    d = 0
    np = 0
    while(flag ==0):
        x+=1
        node = L[0]
        while(node!=None and flag==0):
            i = node.val
            t1 = 0
            t2 = 0
            if ((i-x) in p)==False and ((i-x) in sa)==False:
                p.add(i-x)
                # print('-',x,i,i-x)
                d+=x
                np+=1
                if np==m:
                    flag=1
                    break
                t1 = 1
            if ((i+x) in p)==False and ((i+x) in sa)==False:
                p.add(i+x)
                # print('+',x,i,i+x)
                d+=x
                np+=1
                if np==m:
                    flag=1
                    break
                t2 = 1
            if t1==0 and t2==0:
                node.val,node.next = node.next.val,node.next.next
            else:
                node = node.next

    p = list(p)
    print(d)
    print(' '.join([str(i) for i in p]))
main()