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())
lis = sorted((map(int,input().split())))
aa=[[0]*2 for i in range(200001)]
for i in range(n):
    a=lis[i]
    c=0
    while a>=0:
        if aa[a][0]<k:
            aa[a][0]+=1
            aa[a][1]+=c
        c+=1
        if a==0:
            break
        a=a//2
#    print(aa[:10])
m=1000000000    
for i in range(200001):
    if aa[i][0]==k:
        m=min(m,aa[i][1])
print(m)