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

heap = []
n, m = map(int, input().split(' '))
trees = list(map(int, input().split(' ')))
trees.sort()

data = []
for i in range(n):
  start = trees[i] - 1
  end = trees[i] + 1
  if i > 0 and trees[i - 1] + 1 == trees[i]:
    start = trees[i]
  if i < n - 1 and trees[i] + 1 == trees[i + 1]:
    end = trees[i]
  data.append([trees[i], start, end])

def find(position, start, end):
  if start == position and end == position:
    return (9999999999999999, 9999999999999999)
  elif start == position:
    return (end - position, end)
  elif end == position:
    return (position - start, start)
  target = start
  distance = position - start
  if end - position < distance:
    target = end
    distance = end - position
  return (distance, target)

for i in range(n):
  position = data[i][0]
  start = data[i][1]
  end = data[i][2]
  distance = find(position, start, end)[0]
  heapq.heappush(heap, (distance, i))

result_sum = 0
result_array = []

for i in range(m):
  distance, index = heapq.heappop(heap)
  position = data[index][0]
  start = data[index][1]
  end = data[index][2]
  while distance != find(position, start, end)[0]:
    new_distance = find(position, start, end)[0]
    heapq.heappush(heap, (new_distance, index))
    distance, index = heapq.heappop(heap)
    position = data[index][0]
    start = data[index][1]
    end = data[index][2]
  distance, target = find(position, start, end)
  result_sum += distance
  result_array.append(target)
  if target < position:
    if index > 0 and data[index - 1][2] == data[index][1]:
      data[index - 1][2] = data[index - 1][0]
      data[index][1] = data[index][0]
    else:
      data[index][1] -= 1
  elif target > position:
    if index < n - 1 and data[index + 1][1] == data[index][2]:
      data[index + 1][1] = data[index + 1][0]
      data[index][2] = data[index][0]
    else:
      data[index][2] += 1
  position = data[index][0]
  start = data[index][1]
  end = data[index][2]
  new_distance = find(position, start, end)[0]
  heapq.heappush(heap, (new_distance, index))

print(result_sum)
for i in result_array:
  print(i, end=' ')