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,itertools
from collections import Counter,deque,defaultdict
from bisect import bisect_left,bisect_right 
from heapq import heappop,heappush,heapify, nlargest
from copy import deepcopy
mod = 10**9+7
INF = float('inf')
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))
def inpl_1(): return list(map(lambda x:int(x)-1, sys.stdin.readline().split()))
def err(x): print(x); exit()

n,k = inpl()
a = inpl(); a.sort()
c = Counter(a)
if max(c.values()) >= k: err(0)
aa = [0] + list(itertools.accumulate(a))
res = INF
for x in a:
    want = k - c[x]
    left_cnt = bisect_left(a,x)
    mi_cost = (x-1)*left_cnt-aa[left_cnt] 
    if left_cnt >= want:
        res = min(res, mi_cost+want)
    right_cnt = n-bisect_right(a,x)
    ma_cost = (aa[-1] - aa[-right_cnt-1]) - (x+1)*right_cnt
    if right_cnt >= want:
        res = min(res, ma_cost+want)
    res = min(res, mi_cost+ma_cost+want)
print(res)