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;
const int INF = 2147483647;
const int N = 200005;
int n, k, i, a, miss, s, s2, last;
long long sum, res;
map<int, int> mapa;
map<int, int>::iterator it;
map<int, int>::reverse_iterator rit;
map<int, long long> low, high;
int main() {
  scanf("%d %d", &n, &k);
  for (i = 0; i < n; i++) {
    scanf("%d", &a);
    mapa[a]++;
  }
  for (auto& w : mapa)
    if (w.second >= k) {
      printf("0\n");
      return 0;
    }
  s = 0;
  s2 = 0;
  last = -1;
  sum = 0;
  for (it = mapa.begin(); it != mapa.end(); it++) {
    sum += (it->first - last) * 1LL * s;
    sum += (it->first - last - 1) * 1LL * s2;
    low[it->first] = sum;
    if (last != -1) s += mapa[last];
    s2 = it->second;
    last = it->first;
  }
  s = 0;
  s2 = 0;
  last = -1;
  sum = 0;
  for (rit = mapa.rbegin(); rit != mapa.rend(); rit++) {
    sum += (last - rit->first) * 1LL * s;
    sum += (last - 1 - rit->first) * 1LL * s2;
    high[rit->first] = sum;
    if (last != -1) s += mapa[last];
    s2 = rit->second;
    last = rit->first;
  }
  res = INF * 1LL * INF;
  s = 0;
  for (auto& w : mapa) {
    miss = k - w.second;
    if (w.second + s >= k) res = min(res, low[w.first] + miss);
    if (n - s >= k) res = min(res, high[w.first] + miss);
    res = min(res, low[w.first] + high[w.first] + miss);
    s += w.second;
  }
  printf("%lld\n", res);
  return 0;
}