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:
def reduce(n):
    a = []
    while n>0:
        n=n//2
        a.append(n)
    return a
n,k = list(map(int,input().split()))
a = list(map(int,input().split()))
b = list(set(a))
b.sort()
from collections import defaultdict
c,d = defaultdict(int),defaultdict(int)
c[0]=0
d[0]=0
for i in a:
    c[i]+=1
    d[i]=0
for i in b:
    p,q = c[i],d[i]
    t = reduce(i)
    t.reverse()
    w=1
    while t!=[]:
        r = t.pop()
        x = c[r]
        if x>=k:
            w=w+1
            continue
        else:
            if (x+p)<=k:
                c[r]=x+p
                d[r]+=(w*p)
            else:
                z = k-x
                c[r]=k
                d[r]+=z*w
            w=w+1
mi = float("inf")
for i in c:
    if c[i]>=k:
        if d[i]<mi:
            mi=d[i]
print(mi)