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 PYTHON):

Solution:
from sys import stdin
RI = lambda : map(int,stdin.readline().split())

n,k = RI()
arr = RI()
arr.sort()

maxi = arr[n-k]
ans = 'a'
for i in xrange(maxi+1):
    cnt = 0
    cost = 0
    for j in xrange(n):
        tmp = arr[j]
        xx = 0
        while tmp>i:
            tmp>>=1
            xx+=1
        if tmp==i:
            cnt+=1
            cost+=xx
        if cnt>=k:break

    if cnt >=k:
        if ans=='a': ans = cost
        else: ans = min(ans,cost)
print ans