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;
map<pair<int, int>, int> valuesMap;
int getSteps(int first, int second) {
  if (first < second) {
    return -1;
  }
  if (first == second) {
    return 0;
  }
  int steps = 0;
  while (true) {
    first = first / 2;
    steps++;
    if (first == second) {
      return steps;
    }
    if (first == 0) {
      return -1;
    }
  }
}
int findMin(map<int, int>& iNumbers, int pivot, int k) {
  int res = 0;
  int samesCount = 0;
  for (auto it = iNumbers.begin(); it != iNumbers.end(); it++) {
    int number = it->first;
    if (number < pivot) {
      continue;
    }
    if (valuesMap[{number, pivot}] == 0) {
      samesCount = samesCount + it->second;
      if (samesCount >= k) {
        return res;
      }
      continue;
    }
    if (number > pivot) {
      int curSteps = 0;
      bool isFirstZero = false;
      while (!isFirstZero) {
        curSteps++;
        number = number / 2;
        if (number == 0) {
          isFirstZero = true;
        }
        if (number == pivot) {
          samesCount = samesCount + it->second;
          res = res + curSteps * it->second;
          if (samesCount >= k) {
            return res - (samesCount - k) * curSteps;
          }
        }
        if (number < pivot) {
          break;
        }
      }
    }
  }
  return 1000 * 1000 * 1000;
}
int main() {
  int n;
  cin >> n;
  int k;
  cin >> k;
  if (n == 1 || k == 1) {
    cout << 0;
    return 0;
  }
  map<int, int> numbers;
  for (int i = 0; i < n; i++) {
    int number;
    cin >> number;
    numbers[number]++;
  }
  set<int> candidates;
  candidates.insert(0);
  for (auto it = numbers.begin(); it != numbers.end(); it++) {
    auto number = it->first;
    candidates.insert(number);
    while (number > 0) {
      number = number / 2;
      candidates.insert(number);
    }
  }
  for (auto it = numbers.begin(); it != numbers.end(); it++) {
    for (auto jt = candidates.begin(); jt != candidates.end(); jt++) {
      int value = getSteps(it->first, *jt);
      valuesMap[{it->first, *jt}] = value;
    }
  }
  int ans = 1000 * 1000 * 1000;
  for (auto it : candidates) {
    ans = min(findMin(numbers, it, k), ans);
  }
  cout << ans;
}