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:
n,m=map(int,input().split())
l=list(map(int,input().split()))
l.sort()
d={}
for i in l:
    if i not in d:
        d[i]=1
    else:
        d[i]+=1
e=list(d.keys())
e.append(0)
ans=0
r=1000000000000000
for i in range(0,200001):
    if i in d:
        x=d[i]
    else:
        x=0
    if(x>=m):
        r=0
        break
    ans=0
    for j in l:
        if(j==i):
            continue
        else:
            f=0
            while(j>=i):
                if(j==i or j==0):
                    x+=1
                    ans+=f
                    break
                j//=2
                f+=1
        if(x>=m):
            r=min(ans,r)
            break
print(r)