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;
const int MAXN = 200100;
long long v[MAXN];
long long pre[MAXN], pos[MAXN];
long long q[MAXN], qp[MAXN];
signed main() {
  memset(q, 0, sizeof q);
  memset(qp, 0, sizeof qp);
  long long n, k;
  cin >> n >> k;
  for (long long i = 1; i <= n; i++) cin >> v[i];
  sort(v + 1, v + n + 1);
  v[0] = 0;
  v[n + 1] = 0;
  long long soma = 0;
  for (long long i = 1; i <= n; i++) {
    if (v[i] != v[i - 1]) {
      soma += q[i - 1];
      soma += (i - 1) * (v[i] - v[i - 1] - 1);
      q[i] = i - 1;
    } else
      q[i] = q[i - 1];
    pre[i] = soma;
  }
  soma = 0;
  for (long long i = n; i >= 1; i--) {
    if (v[i] != v[i + 1]) {
      soma += qp[i + 1];
      soma += (n - i) * (v[i + 1] - v[i] - 1);
      qp[i] = n - i;
    } else
      qp[i] = qp[i + 1];
    pos[i] = soma;
  }
  long long resp = -1;
  for (long long i = 1; i <= n; i++) {
    long long res = -1;
    if (i >= k) {
      long long h = i - q[i];
      if (h >= k)
        res = 0;
      else
        res = pre[i] + k - h;
    }
    if (n - i + 1 >= k) {
      long long h = n - i + 1 - qp[i];
      if (h >= k)
        res = 0;
      else if (res == -1)
        res = pos[i] + k - h;
      else
        res = min(res, pos[i] + k - h);
    }
    long long h = n - qp[i] - q[i];
    if (res == -1)
      res = pos[i] + pre[i] + max(k - h, (long long)0);
    else
      res = min(res, pos[i] + pre[i] + max(k - h, (long long)0));
    if (resp == -1)
      resp = res;
    else
      resp = min(resp, res);
  }
  cout << resp << endl;
}