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 count(a, b):
    k = 0
    while(a > b):
        a = a//2
        k+=1
    if a==b:
        return k
    else:
        return None

n, k = input().split()
n = int(n)
k = int(k)
s = list(input().split(" "))
for i in range(n):
    s[i] = int(s[i])
s.sort()
number_of_operations = []
for i in range(1, max(s) + 1):
    sum = 0
    quantity = 0
    for number in s:
        try:
            sum += count(number, i)
            quantity += 1
        except TypeError:
            continue
        if quantity == k:
            number_of_operations.append(sum)
            break
print(min(number_of_operations))
   


"""
f = 0
while(f ==0):
    trend = collections.Counter(s).most_common()
    count = s.count(trend)
    if count == k:
        f = 1
        break

    for i in range(s.index(trend, 0, n)):
        print(i)
        #s[i]/=2
        res+=1


"""