<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 merge(unsigned int i, unsigned int iSize,
    unsigned int j, unsigned int jSize)
    {
        unsigned int low = j, high = j;
        int searched = 0;
        std::vector<long long> newSum;
        for (unsigned int left = i; left <= iSize; ++left)
        {
            while (low <= jSize && sum[low] - sum[left] < lower)
                ++low;
            while (high <= jSize && sum[high] - sum[left] <= upper)
                ++high;
            while (j <= jSize && sum[j] < sum[left])
                newSum.push_back(sum[j]), ++j;
            newSum.push_back(sum[left]);
            searched += high - low;
        }
        while (j <= jSize)
            newSum.push_back(sum[j]), ++j;
        j = 0;
        while (i <= jSize)
            sum[i] = newSum[j], ++i, ++j;
        return searched;
    }
    int mergeSort(unsigned int left, unsigned int right)
    {
        if (left >= right) return 0;
        unsigned int middle = left + (right - left) / 2;
        int i = mergeSort(left, middle);
        int j = mergeSort(middle + 1, right);
        return i + j + merge(left, middle, middle + 1, right);
    }
    int countRangeSum(vector<int>& nums, int lower, int upper)
    {
        this->lower = lower, this->upper = upper;
        unsigned int size = nums.size();
        sum.push_back(0);
        for (unsigned int i = 0; i < size; ++i)
            sum.push_back(sum[i] + nums[i]);
        return mergeSort(0, size);
    }
private:
    int lower, upper;
    std::vector<long long> sum;
};
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