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
def deep(mas, pref, k):
    deepmas = []
    s = 0
    for el in mas:
        if el[:len(pref)] == pref:
            deepmas.append(el)
            if len(deepmas) <= k:
                s += len(el) - len(pref)
    if len(deepmas) >= k:
        return min(s, deep(deepmas, pref + '0', k), deep(deepmas, pref + '1', k))
    else:
        return 20000000000000000

n, k = map(int, input().split())
mas = list(map(int, input().split()))
mas.sort()
mas = list(map(bin, mas))
pref = '0b'
ans = deep(mas, pref, k)
print(ans)
