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;
int n, k;
long long calc(int a, int b) {
  int c = a / b;
  int d = a % b;
  return (long long)(b - d) * c * c + (long long)d * (c + 1) * (c + 1);
}
struct carrot {
  int sum, num;
  long long delta;
  carrot() {}
  carrot(int _a, int _b, long long _c) {
    sum = _a;
    num = _b;
    delta = _c;
  }
  bool operator<(const carrot &a) const { return delta < a.delta; }
};
priority_queue<carrot> pq;
long long ans = 0;
int main() {
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    pq.push(carrot(x, 1, calc(x, 1) - calc(x, 2)));
  }
  int cnt = 1;
  while (cnt <= k - n) {
    cnt++;
    int sum = pq.top().sum;
    int num = pq.top().num;
    int delta = pq.top().delta;
    pq.push(carrot(sum, num + 1, calc(sum, num + 1) - calc(sum, num + 2)));
    pq.pop();
  }
  long long ans = 0;
  while (!pq.empty()) {
    ans += calc(pq.top().sum, pq.top().num);
    pq.pop();
  }
  cout << ans << endl;
  return 0;
}
