<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 lower;
    int upper;
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        this->lower = lower;
        this->upper = upper;
        vector<long long int> sums(nums.size() + 1, 0);
        long long int sum = 0;
        for(int i = 0 ; i < nums.size() ; ++i){
            sum += nums[i];
            sums[i + 1] = sum;
        }

        int ans = mergeSort(sums, 0, sums.size());
        return ans;
    }

    int mergeSort(vector<long long int>& sums, int low, int high){
        if(high - low <= 1){
            return 0;
        }

        int mid = (low + high) / 2;
        int left = mergeSort(sums, low, mid);
        int right = mergeSort(sums, mid, high);
        int mergeCnt = merge(sums, low, high, mid);
        return left + right + mergeCnt;
    }

    int merge(vector<long long int>& sums, int low, int high, int mid){
        int lower_index = mid;
        int higher_index = mid;
        int right = mid;
        int cnt = 0;
        vector<long long int> temp;
        for(int left = low ; left < mid ; ++left){
            while(lower_index < high && sums[lower_index] - sums[left] < this->lower){
                ++lower_index;
            }

            while(higher_index < high && sums[higher_index] - sums[left] <= this->upper){
                ++higher_index;
            }

            cnt += (higher_index - lower_index);
            while(right < high && sums[right] < sums[left]){
                temp.push_back(sums[right]);
                ++right;
            }
            temp.push_back(sums[left]);
        }

        while(right < high){
            temp.push_back(sums[right]);
            ++right;
        }

        move(temp.begin(), temp.end(), sums.begin() + low);
        return cnt;
    }
};
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