<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:
    int solve(vector<long long>&numbers,long long left,long long right,long long lower,long long upper)
    {
        if(left>right)
        {
            return 0;
        }
        if(left==right)
        {
            if(lower<=numbers[left] && numbers[left]<=upper)
            {
                return 1;
            }
            return 0;
        }

        long long middle=(left+right)/2;

        long long solution=(solve(numbers,left,middle,lower,upper)+solve(numbers,middle+1,right,lower,upper));

        vector<long long>first;
        vector<long long>second;

        for(long long index=middle;index>=left;index--)
        {
            long long value=numbers[index];

            if(!first.empty())
            {
                value+=first.back();
            }
            first.push_back(value);
        }

        for(long long index=middle+1;index<=right;index++)
        {
            long long value=numbers[index];

            if(!second.empty())
            {
                value+=second.back();
            }

            second.push_back(value);
        }

        sort(first.begin(),first.end());
        sort(second.begin(),second.end());

        for(long long value:first)
        {
            auto it_lower= lower_bound(second.begin(),second.end(),lower-value);
            auto it_upper=upper_bound(second.begin(),second.end(),upper-value);

            if(it_lower<=it_upper)
            {
                solution+=distance(it_lower,it_upper);
            }
        }

        return solution;
    }
    
    int countRangeSum(vector<int>&_numbers, int lower, int upper) {
        vector<long long> numbers(_numbers.begin(),_numbers.end());
        
        return solve(numbers,0,numbers.size()-1,lower,upper);
    }
};
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