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, math
input = sys.stdin.readline
 
def getInt(): return int(input())
def getVars(): return map(int, input().split())
def getList(): return list(map(int, input().split()))
def getStr(): return input().strip()
## -------------------------------

n, k = getVars()
a = getList()
d = {}
for x in a:
    x2 = x
    num = 0
    while x2 > 0:
        if x2 not in d:
            d[x2] = []
        d[x2].append(num)
        x2 //= 2
        num += 1
minS = -1
##print(d)
for key in d:
    if len(d[key]) >= k:
        dKey = d[key].copy()
        dKey.sort()
        s = sum(dKey[:k])
        if minS == -1:
            minS = s
        else:
            minS = min(minS, s)
print(minS)