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:
arr=dict()
zerolock=[True for i in range(51)]

n,k=input().split()
n=int(n)
k=int(k)
data=list(map(lambda x:int(x),input().split()))
for cc in data:
    if len(arr.get(cc, []))==0:
        arr[cc]=[0]
    else:
        arr[cc].append(0)
count=0
while 1:
    count+=1
    for i in range(n):
        data[i] = data[i] >> 1
        cc=data[i]
        if len(arr.get(cc, [])) == 0:
            arr[cc] = [count]
            if cc==0: zerolock[i]=False
        elif cc!=0:
            arr[cc].append(count)
        elif zerolock[i]:
            arr[cc].append(count)
            zerolock[i]=False
    if sum(data)==0:
        break
ans = -1
for c in arr.values():
    if len(c) >= k:
        tempans = 0
        for i in range(k):
            tempans += c[i]
        if ans != -1:
            ans = min(ans, tempans)
        else:
            ans = tempans
print(ans)