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:
# можно ли a привести к b
def check(a, b):
    answ = 0
    while 1:
        if a == b:
            return answ
        if a > b:
            answ += 1
            a //=2
        else:
            return -1

a = [int(i) for i in input().split()]
n = a[0]
k = a[1]
mas = [int(i) for i in input().split()]
steps = 10000000
for b in range(0, max(mas) + 1):
    buf = []
    for i in mas:
        tmp = check(i, b)
        if tmp >= 0:
            buf.append(tmp)
    
    if len(buf) >= k:
        buf.sort()
        Bsum = 0
        for i in range(k):
            Bsum += buf[i]
        if steps > Bsum:
            steps = Bsum
print(steps)