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:
from collections import Counter

n, k = map(int, input().split())
xs = sorted(map(int, input().split()))

c = Counter(xs)
csuml = 0
lcnt = 0
csumr = sum(xs)
rcnt = len(xs)
ans = csumr

for x, cnt in sorted(c.items()):
    r = max(0, k - cnt)
    if not r:
        ans = 0
        break

    csumr -= x * cnt
    rcnt -= cnt

    ansl = lcnt * (x - 1) - csuml + min(lcnt, r)
    if lcnt < r:
        ansl += csumr - rcnt * (x + 1) + r - lcnt

    ansr = csumr - rcnt * (x + 1) + min(rcnt, r)
    if rcnt < r:
        ansr += lcnt * (x - 1) - csuml + r - rcnt

    ans = min(ans, ansl, ansr)
    csuml += x * cnt
    lcnt += cnt

print(ans)