<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>

typedef long long int ll;

class Solution {
public:
    
    void print(vector<int>& a) {
        for(int x : a) {
            cout<<x<<" ";
        }
        cout<<endl;
    }
    
    int count(vector<ll>& nums, int l1, int r1, int l2, int r2, int lower, int upper, int& ans) {
        // cout<<"("<<l1<<", "<<r1<<") ("<<l2<<", "<<r2<<")"<<endl;
        // print(nums);
        
        
        int j = l2, k = l2;
        for(int i=l1; i<=r1; i++) {
            while(j<=r2 && nums[j] < nums[i] + lower) {
                j++;
            }
            while(k<=r2 && nums[k] <= nums[i] + upper) {
                k++;
            }
            ans += (k-j);
            // cout<<nums[i]<<" "<<ans<<endl;
        }
        // cout<<ans<<endl;
        return ans;
    }
    
    void merge(vector<ll>& nums, int l1, int r1, int l2, int r2) {
        vector<ll> ans;
        
        int i=l1, j=l2;
        while(i<=r1 && j<=r2) {
            if(nums[i] <= nums[j]) {
                ans.push_back(nums[i]);
                i++;
            } else {
                ans.push_back(nums[j]);
                j++;
            }
        }
        
        while(i<=r1) {
            ans.push_back(nums[i]);
            i++;
        }
        while(j<=r2) {
            ans.push_back(nums[j]);
            j++;
        }
        
        int idx = 0;
        for(int i=l1, idx=0; i<=r2; i++, idx++) {
            nums[i] = ans[idx];
        }
    }
    
    void mergeSort(vector<ll>& nums, int lo, int hi, int& lower, int& upper, int& ans) {
        // base case
        if(lo >= hi) {
            return;
        }
        
        int mid = lo + (hi - lo)/2;
        
        mergeSort(nums, lo, mid, lower, upper, ans);
        mergeSort(nums, mid+1, hi, lower, upper, ans);
        
        // Find the answer 
        count(nums, lo, mid, mid+1, hi, lower, upper, ans);
        
        merge(nums, lo, mid, mid+1, hi);
    }
    
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        int n = nums.size(), ans = 0;
        vector<ll> psum(n+1, 0), a(n, 0);
        for(int i=0; i<n; i++) {
            psum[i+1] = nums[i] + psum[i];
        }
        
        mergeSort(psum, 0, n, lower, upper, ans);
    
        return ans;
    }
};
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