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:
import sys
import math
input=sys.stdin.readline

n,k=map(int,input().split())
arr=list(map(int,input().split()))
arr.sort()
l=[[0 for i in range(2)] for j in range((2*(10**5))+1)]
for i in range(n):
    l[arr[i]][1]+=1
    cnt=0
    while(arr[i]>0):
        
        arr[i]=arr[i]//2
        cnt+=1
        if(l[arr[i]][1]<k):
            l[arr[i]][0]+=cnt
            l[arr[i]][1]+=1
ans=100000000000
for i in range(len(l)):
    if(l[i][1]>=k):
        ans=min(ans,l[i][0])
print(ans)