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 
import heapq,bisect

def main():
    n,m = map(int,input().split())
    trees = list(map(int,input().split()))
    trees.sort()

    ans = []
    distance = 0
    heap = []
    visited = set()
    for i in trees:
        visited.add(i)

    for i in trees:
        if i+1 not in visited:
            heapq.heappush(heap,(1,i+1))
        if i-1 not in visited:
            heapq.heappush(heap,(1,i-1))

    while heap:
        curr = heapq.heappop(heap)
        if curr[1] not in visited:
            distance += curr[0]
            ans.append(curr[1])
            visited.add(curr[1])
            if len(ans) == m:
                break

            if curr[1]+1 not in visited:
                index = bisect.bisect(trees,curr[1]+1)
                min_dist = float('inf')
                if index < len(trees):
                    min_dist = min(min_dist,trees[index]-curr[1]-1)
                if index-1 >= 0:
                    min_dist = min(min_dist,curr[1]+1-trees[index-1])

                heapq.heappush(heap,(min_dist,curr[1]+1))

            if curr[1]-1 not in visited:
                index = bisect.bisect(trees,curr[1]-1)
                min_dist = float('inf')
                if index < len(trees):
                    min_dist = min(min_dist,trees[index]-curr[1]+1)
                if index-1 >= 0:
                    min_dist = min(min_dist,curr[1]-1-trees[index-1])

                heapq.heappush(heap,(min_dist,curr[1]-1))
        


    print(distance)
    for i in ans:
        print(i,end = ' ')


main()
