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
input = lambda: sys.stdin.readline().strip()

n, k = map(int, input().split())
ls = list(map(int, input().split()))
ls.sort()
arr = []
for i in ls:
    while i!=0:
        arr.append(i)
        i//=2
    arr.append(0)
arr = list(set(arr))
arr.sort()
cnts = []
m = 10000000000000000000
for x in arr:
    Cnt = 0
    S = 0
    for i in ls:
        cnt = 0
        while i>x:
            i//=2
            cnt+=1
        if i==x and Cnt<k: S+=cnt; Cnt+=1
    if Cnt==k: m = min(m, S)
print(m)