<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 {
    int merge(vector<long>& arr,int start,int mid,int end,int lower,int upper){
        vector<long> left(mid-start+1);
        vector<long> right(end-mid);

        for(int i=0;i<left.size();i++) left[i]=arr[start+i];
        for(int i=0;i<right.size();i++) right[i]=arr[mid+1+i];

        int lefti=0,righti=0,arri=start,ans=0,startAns=0,endAns=0;

        for(int i=0;i<left.size();i++){
            while(startAns<right.size() && right[startAns]-left[i]<lower) startAns++;
            while(endAns<right.size() && right[endAns]-left[i]<=upper) endAns++;

            ans+=(endAns-startAns);
        }

        while(lefti<left.size() && righti<right.size()){
            if(left[lefti]<=right[righti]) arr[arri++]=left[lefti++];
            else arr[arri++]=right[righti++];
        }

        while(lefti<left.size()){
            arr[arri++]=left[lefti++];
        }
        while(righti<right.size()){
            arr[arri++]=right[righti++];
        }

        return ans;
    }
    
    int mergeSort(vector<long>& arr,int start,int end,int lower,int upper){
        if(start>=end){
            return 0;
        }

        int mid=start+((end-start)/2);

        int ans=mergeSort(arr,start,mid,lower,upper);
        ans+=mergeSort(arr,mid+1,end,lower,upper); 
        ans+=merge(arr,start,mid,end,lower,upper);

        return ans;
    }
public:
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        int n=nums.size();
        vector<long> prefix(n+1,0);
        for(int i=0;i<n;i++) prefix[i+1]=nums[i]+prefix[i];
        return mergeSort(prefix,0,n,lower,upper);
    }
};
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