<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>

#include <vector>
#include <map>
#include <set>

using namespace std;

class FenwickTree {
public:
    vector<int> bit;
    int n;

    FenwickTree(int size) {
        n = size;
        bit.resize(n + 1, 0);
    }

    void update(int idx, int val) {
        for (++idx; idx <= n; idx += idx & -idx) {
            bit[idx] += val;
        }
    }

    int query(int idx) {
        int sum = 0;
        for (++idx; idx > 0; idx -= idx & -idx) {
            sum += bit[idx];
        }
        return sum;
    }
};

class Solution {
public:
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        set<long long> allSums;
        long long prefixSum = 0;
        allSums.insert(prefixSum);
        for (int num : nums) {
            prefixSum += num;
            allSums.insert(prefixSum);
            allSums.insert(prefixSum - lower);
            allSums.insert(prefixSum - upper);
        }

        map<long long, int> index;
        int rank = 0;
        for (long long sum : allSums) {
            index[sum] = rank++;
        }

        FenwickTree fenwickTree(rank);
        int count = 0;
        prefixSum = 0;
        fenwickTree.update(index[prefixSum], 1);
        for (int num : nums) {
            prefixSum += num;
            int left = index[prefixSum - upper];
            int right = index[prefixSum - lower];
            count += fenwickTree.query(right) - fenwickTree.query(left - 1);
            fenwickTree.update(index[prefixSum], 1);
        }

        return count;
    }
};

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