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())
a = list(map(int, input().split()))
d = {}
a = sorted(a)
d = max(a)
b = [0] * (d + 1)
dp = [0] * (d + 1)
for _ in range(n):
	i = a[_]
	if b[i] >= k:
		continue
	b[i] += 1
	tc = 0
	while i != 0:
		if b[i // 2] >= k:
			i //= 2
		else:
			tc += 1
			b[i // 2] += 1
			dp[i // 2] += tc
			i //= 2
ans = 1431132213123133123213213231323
for i in range(1, d + 1):
	if b[i] >= k:
		ans = min(ans, dp[i])
print(ans)