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:
def move(n, k, heights):
    heights.sort()
    
    for i in range(n-k+1):
        if heights[i] == heights[i+k-1]:
            return 0
    
    m = heights[n - 1 >> 1]
    a = sum(heights[k-1] - heights[i] for i in range(k)) - sum(heights[i] == heights[k-1] for i in range(k, n))
    b = sum(heights[n-1-i] - heights[n-k] for i in range(k)) - sum(heights[n-i-1] == heights[n-k] for i in range(k, n))
    c = sum(abs(m - heights[i]) for i in range(n)) - (n - k)
      
    return min(a, b, c)

n, k = map(int, input().split())
heights = list(map(int, input().split()))
print(move(n, k, heights))