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:
a,b=list(map(int,input().split()))
array=list(map(int,input().split()))
c=b-1
answer=[]
array.sort()
arr=list(range(1,array[-1]+1))
for it in arr:
    element=it
    current=0
    count=0
    for y in range(0,a):
        copare=array[y]
        if copare<element:
            pass
        elif current==b:
            answer.append(count)
            break
        else:
            moves=0
            flag=5
            while True:
                if copare==element:
                    break
                elif copare<element:
                    flag=6
                    break
                else:
                    copare=int(copare//2)
                    moves+=1
            if flag==6:
                pass
            else:
                count+=moves
                current+=1
    if current==b:
        answer.append(count)
array=array[0:b]
moves=0
for it in array:
    while True:
        if it==0:
            break
        else:
            it=int(it//2)
            moves+=1
answer.append(moves)
print(min(answer))