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 main():
    n,k = map(int,input().split())
    aa = [int(a) for a in input().split()]
    vals = list(zip(aa,[0]*n))
    for a in aa:
        i = 0
        while a > 0:
            i+=1
            a = a//2
            vals.append((a, i))
    vals.sort()
    val = -1
    min = 20*k
    for a,i in vals:
        if a != val:
            vcount = 1
            vsum = i
            val = a
        elif vcount < k:
            vcount += 1
            vsum += i
        if vcount == k and vsum < min:
            min = vsum
    print(min)

if __name__ == "__main__":
    main()