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:
n,k = map(int,raw_input().split())
arr = map(int,raw_input().split())
d1 ={}
d2 = {}
arr.sort()
for i in range(0,2*10**5+1):
    d1[i] = 0
    d2[i] = 0

for i in arr:
    cnt = 0
    if(d2[i]<k):
        d2[i] = d2[i] + 1
    while(i>0):
        i = i/2
        cnt = cnt + 1
        if(d2[i]<k):
            d1[i] = d1[i] + cnt
            d2[i] = d2[i] + 1


import sys
mini = 10**9
for i in range(0,2*10**5+1):
    if(d2[i] == k):
        mini = min(mini,d1[i])

print mini