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;
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long n, k;
  cin >> n >> k;
  vector<long long> arr(n);
  for (auto &u : arr) cin >> u;
  sort(arr.begin(), arr.end());
  map<long long, pair<long long, long long>> mp;
  long long ans = 9e18;
  for (auto u : arr) {
    mp[u].first++;
    if (mp[u].first >= k) ans = min(ans, mp[u].second);
    long long pr = 0;
    while (u) {
      pr++;
      u /= 2;
      mp[u].first++;
      mp[u].second += pr;
      if (mp[u].first >= k) ans = min(ans, mp[u].second);
    }
  }
  cout << ans << "\n";
  return 0;
}