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())
a = list(map(int, input().split()))

poss = []
for i in range(n):
    x = a[i]
    while x > 0:
        if x in poss:
            pass
        else:
            poss.append(x)
        x = x // 2

Ans = float('inf')
for res in poss:
    cnt = []
    ans = 0
    for x in a:
        cur = 0
        while x > res:
            x = x // 2
            cur += 1
        if x == res:
            cnt.append(cur)
    if len(cnt) < k:
        continue
    else:
        cnt = sorted(cnt)
        i = 0
        while i < k:
            ans += cnt[i]
            i += 1
    Ans = min(ans, Ans)
print(Ans)