<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>

#define ll long long int    
class Solution {
public:
    void update(vector<ll>& BIT,int index,int val)
    {
        while(index<=BIT.size()-1)
        {
            BIT[index]+=val;
            index+=(index&(-index));
        }
    } 
    int sum(vector<ll>& BIT,int index)
    {
        int s=0;
        while(index>0)
        {
            s+=BIT[index];
            index-=(index&(-index));
        }
        return s;
    }
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        vector<ll> allvalues;
        set<ll> s;
        vector<ll> prefsum(nums.size()+1,0);
        for(int i=1;i<=nums.size();i++)prefsum[i]=prefsum[i-1]+nums[i-1];
        for(auto a:prefsum)
        {
            s.insert(a);
            s.insert(a-lower);
            s.insert(a-upper);
        }
        for(auto a: s)
        {
            allvalues.push_back(a);
        }
        vector<ll> BIT(allvalues.size()+1,0);
        int ans=0;
        for(auto a: prefsum)
        {
            int left_idx=lower_bound(allvalues.begin(),allvalues.end(),a-upper)-allvalues.begin();
            int right_idx=lower_bound(allvalues.begin(),allvalues.end(),a-lower)-allvalues.begin();
            ans+=sum(BIT,right_idx+1)-sum(BIT,left_idx);
            int idx=lower_bound(allvalues.begin(),allvalues.end(),a)-allvalues.begin();
            update(BIT,idx+1,1);
        }
        return ans;
    }
};
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