Problem: You are given the array a consisting of n elements and the integer k ≤ n.

You want to obtain at least k equal elements in the array a. In one move, you can make one of the following two operations:

  * Take one of the minimum elements of the array and increase its value by one (more formally, if the minimum value of a is mn then you choose such index i that a_i = mn and set a_i := a_i + 1); 
  * take one of the maximum elements of the array and decrease its value by one (more formally, if the maximum value of a is mx then you choose such index i that a_i = mx and set a_i := a_i - 1). 



Your task is to calculate the minimum number of moves required to obtain at least k equal elements in the array.

Input

The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a and the required number of equal elements.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the i-th element of a.

Output

Print one integer — the minimum number of moves required to obtain at least k equal elements in the array.

Examples

Input


6 5
1 2 2 4 2 3


Output


3


Input


7 5
3 3 2 1 1 1 3


Output


4

Solution (in PYTHON3):

Solution:
def main():
    n,k = map(int,input().split())
    arr = list(map(int,input().split()))
    nums = [[0 for i in range(2)] for j in range(2*10**5+1)]
    arr.sort()
    for i in arr:
        moves = 0
        #print('start')
        while i >= 0:
            if nums[i][0] == k:
                break
            nums[i][0] += 1
            nums[i][1] += moves
            moves += 1
            i = i//2
            if i == 0:
                nums[i][0] += 1
                nums[i][1] += moves
                break

    min_moves = float('inf')
    for i in range(2*10**5+1):
        if nums[i][0] >= k:
            min_moves = min(min_moves,nums[i][1])

    print(min_moves)


main()