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,k = map(int,input().split());
arr = list(map(int,input().split()));
tarr = [];
for i in range(n):
    t = arr[i];
    while(t>=1):
        tarr.append(t);
        t = t//2;
ans = 10**9 + 7;   
for i in tarr:
    cnt = [];
    for j in range(n):
        t = arr[j];
        cnt1 = 0;
        while(t//2>=i):
            cnt1+=1;
            t = t//2;
        if(t==i):
            cnt.append(cnt1);
    cnt.sort();
    if(len(cnt)>=k):
        ans=min(ans,sum(cnt[0:k]))
print(ans);