<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;  // binary indexed tree
    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 sum(int r) {
        int ret = 0;
        for (; r >= 0; r = (r & (r + 1)) - 1)
            ret += bit[r];
        return ret;
    }

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

    void add(int idx, int delta) {
        for (; idx < n; idx = idx | (idx + 1))
            bit[idx] += delta;
    }
};

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

        for(int i=0;i<n;i++){
            sum+=nums[i];
            a.push_back({sum,i});
        }
        sort(a.begin(),a.end());
        // [1 ,2, (7), 99], lower = 5, upper = 6
        FenwickTree t(n);
        int L = 0,R=0;
        for(int i = 0;i<n;i++){
            //TODO:Prevent integer overflow
            while(R<n && (a[i].first - a[R].first) >= (1ll*lower)){
                t.add(a[R].second,1);
                R++;
            }
            while(L<n && (a[i].first - a[L].first) > (1ll*upper)){
                t.add(a[L].second,-1);
                L++;
            }
            /*
            for(int j=0;j<n;j++)cout<<t.sum(j,j)<<" \n"[j==n-1];
            cout<<"Get position = "<<a[i].second<<",sum = "<<a[L].first<<", Number of good sums = "<<t.sum(a[i].second-1)<<'\n';
            */

            //prevent counting itself (when lower<=0<=upper)
            ans+=t.sum(a[i].second-1);
            //lower <= sum(nums[0],nums[1],...,nums[i]) <= upper
            if(a[i].first >= lower && a[i].first <= upper)ans++;
        }

        return ans;
    }
};
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