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, k, i, j, a[500], ans = 99999, x;
map<long long, long long> cost, num;
int main() {
  cin >> n >> k;
  for (i = 1; i <= n; i++) {
    cin >> a[i];
  }
  sort(a + 1, a + 1 + n);
  for (i = 1; i <= n; i++) {
    long long x = 0;
    while (a[i] != 0 && num[a[i]] < k) {
      cost[a[i]] += x;
      num[a[i]]++;
      a[i] /= 2;
      x++;
    }
  }
  for (auto p : num) {
    if (p.second == k) {
      ans = min(ans, cost[p.first]);
    }
  }
  cout << ans;
}