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:
import math     
def process(A, n, e):
  B=[]
  D={}
  for i in A:
    k=i
    C=[]
    while k >= 1:
      C.append(k)
      D[k]=D.get(k,0)+1
      k=k//2
    
    B.append(C)
    E=[]
  for i in D.keys():
    if D[i] >= e:
      E.append(i)
 
  # for i in range(len(B)):
  #   print(B[i])

  # print(E)
  res=1e30
  for i in E:   
    F=[]
    for q in range(len(B)):   
      for t in range(len(B[q])):
        if B[q][t]==i:
          F.append(t)
          break
    F.sort()

    
    res=min(res, sum(F[0: e]))
  
    
  return res 
 
n, k=[int(x) for x in input().split()]
A=[int(x) for x in input().split()]
print(process(A, n , k))