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 maxn = 1e6;
const long long maxx = 1e15;
using namespace std;
long long a[maxn];
long long num[maxn], cnt[maxn], pre[maxn], suf[maxn], pcnt[maxn], psuf[maxn];
int m, s;
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 1; i <= n; i++) cin >> a[i];
  sort(a + 1, a + 1 + n);
  for (int i = 1; i <= n; i++) {
    s++;
    if (a[i] != a[i + 1]) {
      m++;
      num[m] = a[i];
      cnt[m] = s;
      s = 0;
    }
  }
  for (int i = 2; i <= m; i++) {
    pre[i] = pre[i - 1] + pcnt[i - 1] * (num[i] - num[i - 1]) +
             cnt[i - 1] * (num[i] - num[i - 1] - 1);
    pcnt[i] = pcnt[i - 1] + cnt[i - 1];
  }
  for (int i = m - 1; i >= 1; i--) {
    suf[i] = suf[i + 1] + psuf[i + 1] * (num[i + 1] - num[i]) +
             cnt[i + 1] * (num[i + 1] - num[i] - 1);
    psuf[i] = cnt[i + 1] + psuf[i + 1];
  }
  long long real = maxx, flag = 0;
  for (int i = 1; i <= m; i++) {
    long long ans1 = maxx, ans2 = maxx, ans3 = maxx;
    int res = k - cnt[i];
    if (res <= 0) {
      cout << "0\n";
      flag = 1;
      break;
    } else {
      if (pcnt[i] - res >= 0) ans1 = pre[i] + res;
      if (psuf[i] - res >= 0) ans2 = suf[i] + res;
      ans3 = pre[i] + suf[i] + res;
      real =
          real < min(ans1, min(ans2, ans3)) ? real : min(ans1, min(ans2, ans3));
    }
  }
  if (flag == 0) cout << real << endl;
  return 0;
}