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= list(map(int,input().split()))
n[0] 
k = n[1]
a = list(map(int,input().split()))
dicta = {}
dictb = {}
for j in a:
    if j in dicta:
        dicta[j]+=1
    else:
        dicta[j]=1
    if j not in dictb:
        dictb[j] = 0  
b=0
for j in dicta:
    if dicta[j]>=k:
        b=1
        break
if b==1:
    print(0)
else:
    minimum = 2*10**5+1
    for i in range(20):
        tmp = []
#         print(a)
        for l in a:
            j = l//2
            if j in dicta:
                dicta[j]+=1
                dictb[j]+=i+1
                if dicta[j]>=k:
                    if dictb[j]<minimum:
                        minimum =dictb[j]
            elif j>0:
                dicta[j]=1
                dictb[j]=i+1
            tmp.append(j)
        a = tmp
        for j in dicta:
            if dicta[j]>=k:
                if dictb[j]<minimum:
                    minimum =dictb[j]
    print(minimum)