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:
n,k=map(int,input().split())
it=list(map(int,input().split()))
a=[[] for i in range(n)]
for i in range(n):
    j=it[i]
    a[i]=[j]
    while True:
        j=j//2
        a[i].append(j)
        if j==0:
            break
ss={}
for i in a:
    for j in i:
        try:
            ss[j]+=1
        except:
            ss[j]=1
mi=10**10
for i in ss:
    if ss[i]>=k:
        l=[-1]*n
        j=0
        for ii in a:
            try:
                l[j]=ii.index(i)
            except:
                pass
            j+=1
        l=[i for i in l if i!=-1]
        l.sort()
        l=l[:k]
     #   if sum(l)<mi:
      #      print(l,i)
        mi=min(mi,sum(l))
print(mi)