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
from sys import stdin,stdout

if __name__ == '__main__':
    n,k=map(int,stdin.readline().split())
    a=list(map(int,stdin.readline().split()))
    ans=200000
    for x in range(0,200001):
        cnt=0
        b=[]
        for V in a:
            v=V
            num=0
            while v>x:
                v//=2
                num+=1
            if v!=x:
                num=200000
            b.append(num)
        b.sort()
        for i in range(k):
            cnt+=b[i]
        ans=min(ans,cnt)
    stdout.write('%d\n'%(ans))




