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;
vector<int> g[200005];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int n, m, i, v, j;
  cin >> n >> m;
  for (i = 1; i <= n; i++) {
    cin >> v;
    int cnt = 0, temp;
    temp = v;
    while (temp > 0) {
      g[temp].push_back(cnt);
      temp /= 2;
      cnt++;
    }
    g[temp].push_back(cnt);
  }
  int ans = 1e9;
  ;
  for (i = 0; i < 200005; i++) {
    if (g[i].size() < m) continue;
    sort(g[i].begin(), g[i].end());
    int cost = 0;
    for (j = 0; j < m; j++) cost += g[i][j];
    ans = min(ans, cost);
  }
  cout << ans << '\n';
  return 0;
}