<p>Given an integer array <code>nums</code> and two integers <code>lower</code> and <code>upper</code>, return <em>the number of range sums that lie in</em> <code>[lower, upper]</code> <em>inclusive</em>.</p>

<p>Range sum <code>S(i, j)</code> is defined as the sum of the elements in <code>nums</code> between indices <code>i</code> and <code>j</code> inclusive, where <code>i &lt;= j</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [-2,5,-1], lower = -2, upper = 2
<strong>Output:</strong> 3
<strong>Explanation:</strong> The three ranges are: [0,0], [2,2], and [0,2] and their respective sums are: -2, -1, 2.
</pre>

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

<pre>
<strong>Input:</strong> nums = [0], lower = 0, upper = 0
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>-10<sup>5</sup> &lt;= lower &lt;= upper &lt;= 10<sup>5</sup></code></li>
	<li>The answer is <strong>guaranteed</strong> to fit in a <strong>32-bit</strong> integer.</li>
</ul>

class Solution {
public:
    int solve(vector<long long> &numbers, long long left, long long right, long long lower, long long upper) {
        if (left > right) {
            return 0;
        }
        if (left == right) {
            if (lower <= numbers[left] && numbers[left] <= upper) {
                return 1;
            }

            return 0;
        }

        long long middle = (left + right) / 2;

        long long solution = (
            solve(numbers, left, middle, lower, upper) +
            solve(numbers, middle + 1, right, lower, upper)
        );

        vector<long long> first;
        vector<long long> second;

        for (long long index = middle; index >= left; index--) {
            long long value = numbers[index];

            if (not first.empty()) {
                value += first.back();
            }

            first.push_back(value);
        }

        for (long long index = middle + 1; index <= right; index++) {
            long long value = numbers[index];

            if (not second.empty()) {
                value += second.back();
            }

            second.push_back(value);
        }

        sort(first.begin(), first.end());
        sort(second.begin(), second.end());

        for (long long value: first) {
            auto it_lower = lower_bound(second.begin(), second.end(), lower - value);
            auto it_upper = upper_bound(second.begin(), second.end(), upper - value);

            if (it_lower <= it_upper) {
                solution += distance(it_lower, it_upper);
            }
        }

        return solution;
    }

    int countRangeSum(vector<int> &_numbers, int lower, int upper) {
        vector<long long> numbers(_numbers.begin(), _numbers.end());

        return solve(numbers, 0, numbers.size() - 1, lower, upper);
    }
};
422766