<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>

struct FenwickTree{
    vector<int> bit;
    int n;

    FenwickTree(int n){
        this->n=n;
        bit.assign(n,0);
    }

    FenwickTree(vector<int> a) : FenwickTree(a.size()){
        for(size_t i=0;i<a.size();i++)
            add(i,a[i]);
    }

    int range_sum(int r){
        int sum=0;
        while(r>=0){
            sum+=bit[r];
            r=(r&(r+1))-1;
        }
        
        return sum;
    }

    int range_sum(int l,int r){
        return range_sum(r)-range_sum(l-1);
    }

    void add(int index,int val){
        while(index<n){
            bit[index]+=val;
            index=index|(index+1);
        }
    }
};

class Solution {
public:
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        vector<pair<long long,int>> a;
        int n=nums.size();
        int ans=0;
        long long sum=0;

        for(int i=0;i<n;i++){
            sum+=nums[i];
            a.push_back({sum,i});
        }
        
        sort(a.begin(),a.end());

        FenwickTree t(n);
        int l=0,r=0;

        for(int i=0;i<n;i++){
            while(r<n and (a[i].first - a[r].first) >= (1LL*lower)){
                t.add(a[r].second,1);
                r++;
            }

            while(l<n and (a[i].first - a[l].first) > (1LL*upper)){
                t.add(a[l].second,-1);
                l++;
            }
            
            ans+=t.range_sum(a[i].second-1);
            if(a[i].first >= lower and a[i].first <= upper)
                ans++;
        }

        return ans;
    }
};
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