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 div(x, a):
    left = -1
    right = 64
    while right - left > 1:
        mid = (right + left) // 2
        if x // pow(2, mid) <= a:
            right = mid
        else:
            left = mid
    return right


n, k = map(int, input().split())
x = [int(x) for x in input().split()]
x.sort()
answer = pow(10, 100)
for i in range(len(x)):
    t = x[i]
    divs = 0
    isDivisible = True
    while isDivisible:
        cnt = 1
        temp = divs
        for j in range(len(x)):
            #print(x[i], ' to ', t,' and ', x[j], ' got ', temp, ' count ', cnt)
            if i == j or x[j] < t or cnt == k:
                continue
            a = div(x[j], t)
            if x[j] // pow(2, a) == t:
                cnt += 1
                temp += a
        if cnt == k:
            answer = min(temp, answer)
        if t == 0:
            isDivisible = False
        t //= 2
        divs += 1
print(answer)