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())
a = list(map(int,input().split()))
mx = int(2e5)
num = [0 for _ in range(mx+1)]
numAdd = [[] for _ in range(mx+1)]
for v in a:
    num[v]+=1
    if(num[v]==m):
        print(0)
        exit()
c=0
for i in range(2,mx+1):
    if num[i]!=0:
        # print('INPUT:',i)
        cur=i
        count = 0
        while(cur!=1):
            next = cur//2
            count+=1;
            add = [count for _ in range(num[i])]
            numAdd[next] = numAdd[next] + add
            # print(next,'NUMAdd:',numAdd[next])
            cur= next

mn= int(8e9)
for i in range(1,mx+1):
    if num[i]+len(numAdd[i])>=m:
        need = m-num[i]
        my = sum(numAdd[i][:need])
        mn = min(mn,my)
print(mn)