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 main():
    m, n = [int(v) for v in input().split()]
    vals = [int(v) for v in input().split()]
    data = []
    for v in vals:
        res = {}
        d = v
        count = 0
        while d != 0:
            res[d] = count
            count += 1
            d = d // 2
        res[d] = count
        data.append(res)
    all_vals = set()
    for d in data:
        all_vals.update(set(d.keys()))
    results = {}
    for k in all_vals:
        sorted_res = sorted([d[k] for d in data if k in d])
        if len(sorted_res)>=n:
            results[k] = sum(sorted_res[0:n])
    print(min(results.values()))

if __name__ == "__main__":
    main()