<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 FenwickTree {
private:
    vector<int> tree;
    int size;

public:
    FenwickTree(int n) : size(n), tree(n + 1, 0) {}

    void update(int index, int delta) {
        while (index <= size) {
            tree[index] += delta;
            index += index & -index;
        }
    }

    int query(int index) {
        int sum = 0;
        while (index > 0) {
            sum += tree[index];
            index -= index & -index;
        }
        return sum;
    }
};

class Solution {
public:
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        int n = nums.size();
        vector<long> prefixSum(n + 1, 0);

        for (int i = 0; i < n; i++) {
            prefixSum[i + 1] = prefixSum[i] + nums[i];
        }

        set<long> allSums;
        for (long x : prefixSum) {
            allSums.insert(x);
            allSums.insert(x - lower);
            allSums.insert(x - upper);
        }

        map<long, int> indexMap;
        int index = 1;
        for (long x : allSums) {
            indexMap[x] = index++;
        }

        FenwickTree fenwickTree(indexMap.size());
        int count = 0;

        for (long x : prefixSum) {
            int leftIndex = indexMap[x - upper];
            int rightIndex = indexMap[x - lower];
            count += fenwickTree.query(rightIndex) -
                     fenwickTree.query(leftIndex - 1);
            fenwickTree.update(indexMap[x], 1);
        }

        return count;
    }
};
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