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,raw_input().split(" "))
arr = map(int,raw_input().split(" "))
arr.sort()

dist = []
for i in range(n-1):
        dist.append(arr[i+1]-arr[i]-1)


def count(v):
        s = 0
        s += 2*v
        for d in dist:
                if d > 2*v:
                        s += 2*v
                else:
                        s += d
        return s

def do(v,num):
        s = (1+v)*v
        ret = []
        for i in range(1,v+1):
                ret.append(arr[0]-i)
                ret.append(arr[-1]+i)
        if num:
                ret.append(arr[0]-v-1)
                num -= 1
        if num:
                ret.append(arr[-1]+v+1)
                num -= 1
        i = 0
        for d in dist:
                if d >2*v:
                        s += (1+v)*v
                        for j in range(v):
                                ret.append(arr[i]+j+1)
                                ret.append(arr[i+1]-j-1)
                        if num:
                                ret.append(arr[i]+v+1)
                                num -= 1
                        if num and d!=2*v+1:
                                ret.append(arr[i+1]-v-1)
                                num -= 1
                else:
                        p = d/2
                        s += (1+p)*p+(d%2)*((d+1)/2)
                        for j in range(d):
                                ret.append(arr[i]+j+1)

                i += 1
        return ret,s


low,high = 1,m/2+1
while low <= high:
        mid = (low+high)/2
        if count(mid)< m:
                low = mid+1
        else:
                high = mid - 1

num = m-count(low-1)
ret,s1 = do(low-1,num)
ret.sort()

print s1+num*low
print " ".join(map(str,ret))
