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
from collections import defaultdict

ma = defaultdict(list)

def solve(arr, n, k):
	global ma
	
	for a in arr:
		cnt = 0
		while a > 0:
			ma[a].append(cnt)
			a >>= 1
			cnt += 1
	
	ret = 10**10

	for key in ma.keys():
		b = ma[key]

		if len(b) >= k:
			b.sort()
			ret = min(ret, sum(b[:k]))


	return ret


def main():
	n,k = list(map(int, input().strip().split()))

	arr = list(map(int, input().strip().split()))

	print (solve(arr, n, k))

if __name__ == "__main__":
	main()
