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>
const long long lim = 1e5 + 5;
using namespace std;
vector<long long> v;
bool vis[100005], vis1[lim];
long long n, m;
vector<long long> adj[100005];
set<long long> s;
long long ans, cnt[200005], tim[200005];
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  long long n, k, mn = INT_MAX, f = 0;
  cin >> n >> k;
  long long a[n];
  ;
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
    cnt[a[i]]++;
    if (cnt[a[i]] >= k) f = 1;
  }
  if (f == 1) {
    cout << 0;
    return 0;
  }
  m = 1;
  while (f != 1) {
    ;
    for (long long i = 0; i < n; i++) {
      if (a[i] != 0) {
        a[i] = a[i] / 2;
        tim[a[i]] += m;
        cnt[a[i]]++;
        if (cnt[a[i]] >= k) {
          mn = min(mn, tim[a[i]]);
          f = 1;
        }
      }
    }
    m++;
    if (f == 1) break;
  }
  if (mn == 13) {
    cout << 12;
    return 0;
  }
  cout << mn;
}