<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:
    vector<int> segment;
    void updateSegmentTree(int curr, int left, int right, int pos){
        if(left == right){
            segment[curr]++;
            return;
        }
        int mid = left + (right - left)/2;
        if(pos<=mid) updateSegmentTree(2*curr+1,left,mid,pos);
        else updateSegmentTree(2*curr+2,mid+1,right,pos);
        segment[curr] = segment[2*curr+1] + segment[2*curr+2];
    }
    int querySegmentTree(int curr, int left, int right, int ogl, int ogr){
        if(left > ogr || right < ogl) return 0;
        if(left >= ogl && right <= ogr) return segment[curr];
        int mid = left + (right - left)/2;
        return querySegmentTree(2*curr+1,left,mid,ogl,ogr) + querySegmentTree(2*curr+2,mid+1,right,ogl,ogr);
    }
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        vector<long long> prefix(nums.size()+1,0);
        for(int i=0;i<nums.size();i++) prefix[i+1] = prefix[i] + nums[i];
        vector<long long> s(prefix.begin(),prefix.end());
        sort(s.begin(),s.end());
        unordered_map<long long,int> rank;
        int r = 0,ans = 0;
        for(auto& i: s){
            rank[i] = r++;
        }
        int n = r;
        segment.resize(n*4,0);
        for(int i=0;i<prefix.size();i++){
            int left = lower_bound(s.begin(), s.end(), prefix[i] - upper) - s.begin();
            int right = upper_bound(s.begin(), s.end(), prefix[i] - lower) - s.begin() - 1;
            if (left <= right) {
                ans += querySegmentTree(0,0,n-1,left,right);
            }
            updateSegmentTree(0,0,n-1,rank[prefix[i]]);
        }
        return ans;
    }
};
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