There are some rabbits in Singapore Zoo. To feed them, Zookeeper bought n carrots with lengths a_1, a_2, a_3, …, a_n. However, rabbits are very fertile and multiply very quickly. Zookeeper now has k rabbits and does not have enough carrots to feed all of them. To solve this problem, Zookeeper decided to cut the carrots into k pieces. For some reason, all resulting carrot lengths must be positive integers.

Big carrots are very difficult for rabbits to handle and eat, so the time needed to eat a carrot of size x is x^2.

Help Zookeeper split his carrots while minimizing the sum of time taken for rabbits to eat the carrots.

Input

The first line contains two integers n and k (1 ≤ n ≤ k ≤ 10^5): the initial number of carrots and the number of rabbits.

The next line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6): lengths of carrots.

It is guaranteed that the sum of a_i is at least k.

Output

Output one integer: the minimum sum of time taken for rabbits to eat carrots.

Examples

Input


3 6
5 3 1


Output


15


Input


1 4
19


Output


91

Note

For the first test, the optimal sizes of carrots are \{1,1,1,2,2,2\}. The time taken is 1^2+1^2+1^2+2^2+2^2+2^2=15

For the second test, the optimal sizes of carrots are \{4,5,5,5\}. The time taken is 4^2+5^2+5^2+5^2=91.
#include <bits/stdc++.h>
struct Item {
  long long gain;
  int index;
};
const int MAXN = 100005;
int n, k;
int a[MAXN];
int cuts[MAXN] = {};
long long calcCost(long long amt, int cuts) {
  long long base = amt / cuts;
  long long higher = amt % cuts;
  long long lower = cuts - higher;
  long long ans = 0;
  ans += (long long)base * base * lower;
  ans += (long long)(base + 1) * (base + 1) * higher;
  return ans;
}
long long calcGain(long long amt, int cuts) {
  return calcCost(amt, cuts) - calcCost(amt, cuts + 1);
}
int main() {
  scanf("%d %d", &n, &k);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    cuts[i] = 1;
  }
  auto pqcmp = [](const Item &i1, const Item &i2) { return i1.gain < i2.gain; };
  std::priority_queue<Item, std::vector<Item>, decltype(pqcmp)> pq(pqcmp);
  for (int i = 0; i < n; i++) {
    pq.push({calcGain(a[i], cuts[i]), i});
  }
  for (int i = n; i < k; i++) {
    auto item = pq.top();
    pq.pop();
    cuts[item.index]++;
    pq.push({calcGain(a[item.index], cuts[item.index]), item.index});
  }
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    ans += calcCost(a[i], cuts[i]);
  }
  printf("%I64d\n", ans);
  return 0;
}
