<p>You have an <code>inventory</code> of different colored balls, and there is a customer that wants <code>orders</code> balls of <strong>any</strong> color.</p>

<p>The customer weirdly values the colored balls. Each colored ball&#39;s value is the number of balls <strong>of that color&nbsp;</strong>you currently have in your <code>inventory</code>. For example, if you own <code>6</code> yellow balls, the customer would pay <code>6</code> for the first yellow ball. After the transaction, there are only <code>5</code> yellow balls left, so the next yellow ball is then valued at <code>5</code> (i.e., the value of the balls decreases as you sell more to the customer).</p>

<p>You are given an integer array, <code>inventory</code>, where <code>inventory[i]</code> represents the number of balls of the <code>i<sup>th</sup></code> color that you initially own. You are also given an integer <code>orders</code>, which represents the total number of balls that the customer wants. You can sell the balls <strong>in any order</strong>.</p>

<p>Return <em>the <strong>maximum</strong> total value that you can attain after selling </em><code>orders</code><em> colored balls</em>. As the answer may be too large, return it <strong>modulo </strong><code>10<sup>9 </sup>+ 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/05/jj.gif" style="width: 480px; height: 270px;" />
<pre>
<strong>Input:</strong> inventory = [2,5], orders = 4
<strong>Output:</strong> 14
<strong>Explanation:</strong> Sell the 1st color 1 time (2) and the 2nd color 3 times (5 + 4 + 3).
The maximum total value is 2 + 5 + 4 + 3 = 14.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> inventory = [3,5], orders = 6
<strong>Output:</strong> 19
<strong>Explanation: </strong>Sell the 1st color 2 times (3 + 2) and the 2nd color 4 times (5 + 4 + 3 + 2).
The maximum total value is 3 + 2 + 5 + 4 + 3 + 2 = 19.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= inventory.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= inventory[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= orders &lt;= min(sum(inventory[i]), 10<sup>9</sup>)</code></li>
</ul>

#define ull unsigned long long

class Solution {
public:
    int MOD = 1000000007;

    ull summation(int n, int diff) {
        ull nn = (ull) n;
        ull nnd = (ull) (n - diff);

        ull res1 = (nn * (nn+1)) / 2;
        ull res2 = (nnd * (nnd+1)) / 2;

        return ((res1 - res2) % MOD);
    }

    int maxProfit(vector<int>& inventory, int orders) {
        ull res = 0;
        sort(inventory.begin(), inventory.end());
        stack<pair<int, int>> s;
        s.push({0, 0});

        for(int i: inventory) {
            auto [count, groups] = s.top();
            
            if(i > count) {
                s.push({i, 1});
                continue;
            }

            s.pop();
            s.push({ i, groups+1 });
        }

        // while(s.size()) {
        //     auto [cnt, grp] = s.top();
        //     s.pop();
        //     cout << cnt << " " << grp << endl;
        // }

        while( orders && orders >= s.top().second ) {
            auto [fcount, fgroups] = s.top();
            s.pop();
            auto [scount, sgroups] = s.top();
            s.pop();

            cout << "orders = " << orders << endl;
            cout << fcount << " " << fgroups << endl;
            cout << scount << " " << sgroups << endl;

            int diff = fcount - scount;
            int temp = orders % fgroups;
            orders -= temp;

            int inst = orders / fgroups;
            inst = min(inst, diff);

            orders -= fgroups * inst;
            orders += temp;
            res = (
                res +
                ( summation(fcount, inst) * fgroups ) % MOD
            ) % MOD;

            fcount -= inst;

            if(fcount == scount) {
                s.push({ fcount, fgroups + sgroups });
            }

            else {
                s.push({ scount, sgroups });
                s.push({ fcount, fgroups });
            }
            
            cout << "orders = " << orders << endl;
            cout << "res = " << res << endl;
            cout << endl;
        }

        if(orders) {
            res = (res + (ull) orders * s.top().first);
            orders = 0;
        }

        return (int) (res % MOD);
    }
};
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