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>
using namespace std;
uint64_t calcTime(const uint64_t len, const uint64_t parts) {
  uint64_t elem2 = len / parts;
  uint64_t cnt2 = len % parts;
  uint64_t elem1 = elem2++;
  uint64_t cnt1 = parts - cnt2;
  return (cnt1 * elem1 * elem1 + cnt2 * elem2 * elem2);
}
struct stick {
  uint64_t len, parts;
  stick(uint64_t l, uint64_t p) : len(l), parts(p) {}
  stick(uint64_t l) : len(l), parts(1) {}
  bool operator>(const stick& other) const {
    uint64_t score1 = calcTime(len, parts) - calcTime(len, parts + 1);
    uint64_t score2 =
        calcTime(other.len, other.parts) - calcTime(other.len, other.parts + 1);
    return score1 > score2;
  }
  bool operator<(const stick& other) const {
    uint64_t score1 = calcTime(len, parts) - calcTime(len, parts + 1);
    uint64_t score2 =
        calcTime(other.len, other.parts) - calcTime(other.len, other.parts + 1);
    return score1 < score2;
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  uint32_t N, K, len;
  cin >> N >> K;
  priority_queue<stick> carrots;
  for (uint32_t i = 0; i < N; i++) {
    cin >> len;
    carrots.emplace(len);
  }
  while (N != K) {
    stick top = carrots.top();
    carrots.pop();
    top.parts++;
    N++;
    carrots.emplace(top);
  }
  uint64_t t = 0;
  while (!carrots.empty()) {
    const stick& ref = carrots.top();
    t += calcTime(ref.len, ref.parts);
    carrots.pop();
  }
  cout << t;
  return 0;
}
