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 divide(n, x):
    res = 0
    while(n > x):
        n = n//2
        res += 1
    return res,n

def comp(x, a, idx):
    add = 0
    inc = 0
    check = x
    res = 1000000000
    flag = 0
    for j in range(idx+1,n):
        if inc >= k-1:
            flag = 1
            res = min(res,add)
            break
        count,x = divide(a[j],check)
        if x == check:
            add += count
            inc += 1
    if inc >= k-1:
        flag = 1
        res = min(res,add)
    if flag == 0:
        return -1
    else:
        return res
    
n,k = map(int, input().split(" "))
a = list(map(int, input().split(" ")))
a = sorted(a)
res = 1000000000
for i in range(n):
    counter = 0
    temp = 0
    lol = a[i]
    while(lol > 0):
        temp = comp(lol,a,i)
        if temp >= 0:
            res = min(res,temp+counter)
        lol = lol//2
        counter += 1
print(res)