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>
template <typename T>
void scan(T &x) {
  x = 0;
  bool _ = 0;
  T c = getchar();
  _ = c == 45;
  c = _ ? getchar() : c;
  while (c < 48 || c > 57) c = getchar();
  for (; c < 48 || c > 57; c = getchar())
    ;
  for (; c > 47 && c < 58; c = getchar()) x = (x << 3) + (x << 1) + (c & 15);
  x = _ ? -x : x;
}
template <typename T>
void printn(T n) {
  bool _ = 0;
  _ = n < 0;
  n = _ ? -n : n;
  char snum[65];
  int i = 0;
  do {
    snum[i++] = char(n % 10 + 48);
    n /= 10;
  } while (n);
  --i;
  if (_) putchar(45);
  while (i >= 0) putchar(snum[i--]);
}
template <typename First, typename... Ints>
void scan(First &arg, Ints &...rest) {
  scan(arg);
  scan(rest...);
}
template <typename T>
void print(T n) {
  printn(n);
  putchar(10);
}
template <typename First, typename... Ints>
void print(First arg, Ints... rest) {
  printn(arg);
  putchar(32);
  print(rest...);
}
using namespace std;
using ll = long long;
using pii = pair<ll, int>;
const int MM = 1e5 + 5;
int n, k, cnt[MM];
ll a[MM];
priority_queue<pii> q;
ll val(ll s, int d) {
  ll v = s / d, rem = s % d;
  ll ret = rem * (v + 1) * (v + 1) + (d - rem) * v * v;
  return ret;
}
ll go(int i) { return val(a[i], cnt[i]) - val(a[i], cnt[i] + 1); }
int main() {
  scan(n, k);
  for (int i = 0; i < n; i++) {
    scan(a[i]);
    cnt[i] = 1;
    q.emplace(go(i), i);
  }
  k -= n;
  while (k--) {
    int i = q.top().second;
    q.pop();
    cnt[i]++;
    q.emplace(go(i), i);
  }
  ll ans = 0;
  for (int i = 0; i < n; i++) {
    ans += val(a[i], cnt[i]);
  }
  print(ans);
}
