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:
import sys
input = sys.stdin.readline


def main():
    N, K = map(int, input().split())
    A = list(map(int, input().split()))

    M = max(A)
    scores = [[] for _ in range(M+1)]

    for a in A:
        c = 0
        while a > 0:
            scores[a].append(c)
            a //= 2
            c += 1
        scores[0].append(c)

    for a, L in enumerate(scores):
        if len(L) < K: continue
        L.sort()
        if a == 0:
            ans = sum(L[:K])
        else:
            ans = min(ans, sum(L[:K]))

    print(ans)

if __name__ == "__main__":
    main()