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;
template <typename T>
inline void read(T &x) {
  x = 0;
  char c = getchar(), f = 0;
  for (; c < 48 || c > 57; c = getchar())
    if (!(c ^ 45)) f = 1;
  for (; c >= 48 && c <= 57; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
  f ? x = -x : x;
}
const int N = 200005;
int n, K, a[N], cnt[N];
long long qz[N], hz[N];
int main() {
  read(n), read(K);
  for (int i = 1; i <= n; i++) read(a[i]);
  sort(a + 1, a + n + 1);
  for (int i = n; i; i--) hz[i] = hz[i + 1] + a[i];
  for (int i = 1; i <= n; i++) qz[i] = qz[i - 1] + a[i];
  for (int i = 1; i <= n; i++) qz[i] = 1ll * a[i] * i - qz[i];
  for (int i = n; i; i--) hz[i] = hz[i] - 1ll * a[i] * (n - i + 1);
  for (int i = 1; i <= n; i++) cnt[i] = (a[i] == a[i - 1]) * cnt[i - 1] + 1;
  long long res = 1e18;
  for (int i = 1; i <= n; i++)
    if (cnt[i] >= K) return puts("0"), 0;
  for (int i = 1; i <= n; i++) {
    if (i < K)
      res = min(res, qz[i] + hz[i] - n + K);
    else
      res = min(res, qz[i] - i + K);
    if (i > n - K + 1)
      res = min(res, qz[i] + hz[i] - n + K);
    else
      res = min(res, hz[i] - n + i + K - 1);
  }
  return printf("%lld\n", res), 0;
}