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 get_ans(n, k, array):
    logging = {0:[]}
    for i in array:
        steps = 0
        temp = i
        while temp > 0:
            if temp not in logging.keys():
                logging[temp] = [steps]
            else:
                logging[temp].append(steps)
            temp = temp // 2
            steps +=1
        logging[0].append(steps)
    
    ans = sum(logging[0])
    for key, values in logging.items():
        if len(values) >= k:
            temp_ans = sum(sorted(values)[0:k])
            if temp_ans < ans:
                ans = temp_ans
        

    return ans
n, k = list(map(int, input().strip().split()))
array = list(map(int, input().strip().split()))
print(get_ans(n, k, array))