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 func(fr,to):
  global arr2
  if fr==to:
    return 0
  if fr<to:
    return -1
  temp=func(fr//2,to)
  if temp==-1:
    return temp
  return temp+1
n,k=map(int,input().split())
gans=-1
arr=sorted(list(map(int,input().split())))
ss=set()
ss.add(0)
for i in arr:
  temp=i
  while temp>0:
    ss.add(temp)
    temp=temp//2
for i in sorted(ss):
    cs=0
    tk=0
    for j in arr:
        if tk>=k:
            break
        temp=func(j,i)
        if temp<0:
            continue
        cs=cs+temp
        tk=tk+1
    if gans==-1:
        gans=cs
    else:
        if tk>=k:
            gans=min(gans,cs)
    #print(i,cs,tk,gans)
    #print(i,cs,tk)
print(gans)