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())
a=list(map(int,input().split()))
ans=[[0,0] for i in range(200001)]
a.sort()
for i in range(n):
    ans[a[i]][0]+=1
for i in range(n):
    s=a[i]
    d=1
    while (s>0):
        s=s//2
        if ans[s][0]<k:
            ans[s][0]+=1
            ans[s][1]+=d
        d+=1
mi=100000000
for i in range(len(ans)):
    if ans[i][0]>=k:
        if ans[i][1]<mi:
            mi=ans[i][1]
print(mi)