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:
# -*- coding: utf-8 -*-
"""
Created on Mon Jul 27 05:12:54 2020

@author: Dark Soul
"""

MAX=int(2*1e5)+1
arr=[0]*MAX
cnt=[0]*MAX
INF=int(1e8)
[n,k]=list(map(int, input().split()))
x=list(map(int, input().split()))
x.append(0)
x.sort()
flag=0
for i in range(1,n+1):
    arr[x[i]]+=1
    if arr[x[i]]>=k:
        flag=1
if flag:
    print(0)
else:
    sol=INF
    for i in range(1,n+1):
        totop=0
        while x[i]:
            totop+=1
            x[i]=x[i]//2
            cnt[x[i]]+=totop
            arr[x[i]]+=1
            if arr[x[i]]>=k:
                sol=min(sol,cnt[x[i]])
    print(sol)