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:
n, k = map(int, input().split())
arr = []
for i in sorted(map(int, input().split())):
	if not arr or arr[-1][0] != i:
		arr.append([i, 1])
	else:
		arr[-1][1] += 1

costSum = []
countSum = []
for i, count in arr:
	if costSum:
		costSum.append(costSum[-1] + count * i)
		countSum.append(countSum[-1] + count)
	else:
		costSum.append(count * i)
		countSum.append(count)

# print(arr)
# print(countSum)
# print(costSum)

if len(arr) > 1 and k > arr[0][1] and k > arr[-1][1]:
	res = min(costSum[-1] - costSum[0] - (countSum[-1] - countSum[0]) * arr[0][0] - countSum[-1] + k, arr[-1][0] * countSum[-2] - costSum[-2] - countSum[-1] + k)
	# print(costSum[-1] - costSum[0] - (countSum[-1] - countSum[0]) * arr[0][0] - countSum[-1] + k, arr[-1][0] * countSum[-2] - costSum[-2] - countSum[-1] + k)
else:
	res = 0

for i in range(1, len(arr) - 1):
	cost = 0
	fromLeft = arr[i][0] * countSum[i] - costSum[i]
	fromRight = costSum[-1] - costSum[i] - arr[i][0] * (countSum[-1] - countSum[i])
	# print(i, fromLeft, fromRight)
	if countSum[i] < k:
		cost = fromLeft + fromRight + k - countSum[-1]
	elif arr[i][1] < k:
		cost = fromLeft + k - countSum[i]
	# print(cost)
	if countSum[-1] - countSum[i-1] >= k and arr[i][1] < k:
		cost = min(cost, fromRight + k - countSum[-1] + countSum[i-1])
	if res > cost:
		res = cost

print(res)