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 PYTHON):

Solution:
n,k = map(int, raw_input().split())
aas = map(int, raw_input().split())

from collections import defaultdict

# reachable[a] = number of a[i]s that can reach the value a
# costs[a,cost] = number of a[i]s that can reach the value a with a given cost
costs = defaultdict(int)
reachable = defaultdict(int)
for a in aas:
	cost = 0
	while a >= 0:
		costs[a,cost] += 1
		reachable[a] += 1
		cost += 1
		if a == 0:
			break
		a /= 2

#print costs
#print reachable

least_so_far = 100000000000000000000000000
for a in reachable:
	if reachable[a] >= k:
		least_cost_to_a = 0
		total_reached = 0
		for i in xrange(30):
			if 2**(i-2)>2*10**5:
				break
			if total_reached + costs[a,i] >= k:
				remaining = k - total_reached
				least_cost_to_a += remaining*i
				least_so_far = min(least_so_far, least_cost_to_a)
				break
			else:
				total_reached += costs[a,i]
				least_cost_to_a += i*costs[a,i]


print least_so_far