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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long n, m, a[200010], f[200010], l, r, mid, x, y;
int main() {
  scanf("%I64d%I64d", &n, &m);
  for (int i = 1; i <= n; i++) scanf("%I64d", &a[i]);
  sort(a + 1, a + n + 1);
  a[0] = a[1];
  a[n + 1] = a[n];
  f[1] = a[1];
  long long ans = (long long)1e17;
  for (int i = 2; i <= n; i++) f[i] = f[i - 1] + a[i];
  for (int i = 1; i <= n; i++) {
    x = y = 0;
    if (i + m - 1 <= n) {
      x += f[i + m - 1] - f[i - 1] - a[i] * m;
      if (a[i + m - 1] > a[i])
        x += f[n] - f[i + m - 1] - (a[i] + 1) * (n - i - m + 1);
    } else {
      x += (f[n] - f[i - 1]) - a[i] * (n - i + 1);
      x += a[i] * (i - n + m) - (f[i] - f[n - m]);
      if (a[n - m + 1] < a[i]) x += (a[i] - 1) * (n - m) - f[n - m];
    }
    if (i - m + 1 >= 1) {
      y += a[i] * m - (f[i] - f[i - m]);
      if (a[i - m + 1] < a[i]) y += (a[i] - 1) * (i - m) - (f[i - m]);
    } else {
      y += a[i] * (i) - (f[i]);
      y += (f[m] - f[i - 1]) - a[i] * (m - i + 1);
      if (a[m] > a[i]) y += f[n] - f[m] - (a[i] + 1) * (n - m);
    }
    ans = min(ans, min(x, y));
  }
  if (m == 1) ans = 0;
  printf("%I64d", ans);
}